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Analytic results for some types of Feynman integrals at any loop order 认领 引用
1
作者 Bing-Yan Dai Zi-Qiang Chen Long-Bin Chen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第10期166-173,共8页
In this paper,we investigate three types of Feynman integrals up to any loop,including the massless banana integral,the one-mass banana integral,and the massless three-point multi-edge integral.Although these integral... In this paper,we investigate three types of Feynman integrals up to any loop,including the massless banana integral,the one-mass banana integral,and the massless three-point multi-edge integral.Although these integrals are simple in topology,they are involved in many interesting processes,like heavy quarks production and decay,as well as massless quark gluon form factors.By using one-loop integration formulas recursively,we obtain the analytic results at any loop order.It turns out that the results are quite simple and compact.The calculation method used in this work is straightforward,and may be generalized to more general cases. 展开更多
关键词 analytic results uniform transcendental basis Feynman integrals
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A sharp lower bound for the weighted Lehmer mean involving complete p-elliptic integrals 认领 引用
2
作者 ZHAO Tie-hong CHU Yu-ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2025年第3期558-569,共12页
In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic inte... In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic integrals. 展开更多
关键词 Holder mean weighted Lehmer mean complete p-elliptic integrals
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AN EXTENSION OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS 认领 引用
3
作者 Huoxiong WU Lin WU 《Acta Mathematica Scientia》 SCIE CSCD 2025年第3期789-808,共20页
This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω i... This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on Rnwith mean value zero in the unit sphere Sn-1,Under the assumption that Ω∈L∞(Sn-1),the authors establish the Lq-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0. 展开更多
关键词 Marcinkiewicz integral rough kernel uniform estimates Apweight
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A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES 认领 引用 被引量：1
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作者 Hung Viet LE 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1331-1344,共14页
Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that... Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R. 展开更多
关键词 singular integrals Marcinkiewicz integrals mixed smoothness Triebel-Lizorkin spaces
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Boundedness of singular integrals along surfaces on Lebesgue spaces 认领 引用 被引量：2
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作者 ZHANG Yan-dan CHEN Jie-cheng ZHANG Chun-jie 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2010年第2期192-198,共7页
In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications o... In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality. 展开更多
关键词 Singular integrals surfaces rough kernels Plancherel＇s theorem oscillatory singular integrals.
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MONOTONICITY,CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS 认领 引用 被引量：5
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作者 Miaokun WANG Wen ZHANG Yuming CHU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1440-1450,共11页
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
关键词 Gaussian hypergeometric function generalized elliptic integrals convexity inequality
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ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS 认领 引用 被引量：3
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作者 Ronghui LIU Feng LIU Huoxiong WU 《Acta Mathematica Scientia》 SCIE CSCD 2021年第1期241-256,共16页
This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along"polynomial curves".Under the assumption that the kernels satisfy certain rather weak size conditions on t... This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along"polynomial curves".Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness,the authors prove that such operators are bounded on the mixed radial-angular spaces.Meanwhile,corresponding vector-valued versions are also obtained. 展开更多
关键词 Marcinkiewicz integrals rough kernels mixed radial-angular spaces
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Weighted Estimates for Marcinkiewicz Integrals with Non-Doubling Measures 认领 引用 被引量：6
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作者 Songbai WANG Yinsheng JIANG Baode LI 《Journal of Mathematical Research with Applications》 CSCD 2012年第2期223-234,共12页
Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the bounded... Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~. 展开更多
关键词 maximal singular integrals Muckenhoupt type weights sharp maximal operators non-doubling measures.
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Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model 认领 引用 被引量：12
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS 2008年第10期893-896,共4页
The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate fr... The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems. 展开更多
关键词 functional integrals variational-cumulant expansion sine-Gordon Thirring model
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Rough singular integrals associated with surfaces of Van der Corput type 认领 引用 被引量：2
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作者 LIU Feng WU Huo-xiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第1期86-100,共15页
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the f... In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）. 展开更多
关键词 42B20 42B25 42B30 Singular integrals surfaces of Van der Corput type maximal operators Littlewood-Paley theory, Fourier transform estimates
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Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time 认领 引用 被引量：8
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS 2009年第9期445-448,共4页
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum f... The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background. 展开更多
关键词 functional integrals quantum fluctuations noncommutative space-time
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Functional Integrals and Excitation Energy in Three-Band Hubbard Model 认领 引用 被引量：6
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作者 YAN Jun 《Communications in Theoretical Physics》 SCIE CAS 2008年第3期567-570,共4页
The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum a... The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation. 展开更多
关键词 functional integrals Green＇s functions excitation energy Hubbard model
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THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES 认领 引用 被引量：1
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作者 韩妍妍 伍火熊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期1981-1996,共16页
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th... This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn). 展开更多
关键词 fractional type Marcinkiewicz integrals commutators Muckenhoupt weights BMO spaces Hardy spaces
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The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces 认领 引用 被引量：1
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作者 Dan Xiao Lisheng Shu 《Analysis in Theory and Applications》 CSCD 2023年第2期163-177,共15页
Under some natural regularity assumptions on the exponent function,we obtain the boundedness of Marcinkiewicz integralsμ,μsρandμλ*,ρon grand variable Herz spaces.Our results enrich and improve some p... Under some natural regularity assumptions on the exponent function,we obtain the boundedness of Marcinkiewicz integralsμ,μsρandμλ*,ρon grand variable Herz spaces.Our results enrich and improve some previous results in the literature. 展开更多
关键词 Marcinkiewicz integrals Herz spaces variable exponent grand spaces
SINGULAR INTEGRALS ALONG SURFACES ON PRODUCT DOMAINS 认领 引用 被引量：3
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作者 Hussain Al-Qassem 《Analysis in Theory and Applications》 2004年第2期99-112,共14页
In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding ... In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces. 展开更多
关键词 singular integrals product domains rough kernels Block spaces
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The Calculation of Parameters for DNA Kinetic Structure Based on Monte-Carlo Multiple Integrals 认领 引用 被引量：1
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作者 崔向军 蔡禄 《Agricultural Science & Technology》 CAS 2010年第5期5-6,16,共2页
Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA ... Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results. 展开更多
关键词 Monte-Carlo method Multiple integrals DNA Time complexity Precision
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Peano Derivatives and Singular Integrals of Arbitrary Order 认领 引用 被引量：2
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作者 Lu Jianke 《Wuhan University Journal of Natural Sciences》 CAS 1996年第1期9-13,共5页
The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals ... The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established. 展开更多
关键词 Peano derivatives singular integrals of arbitrary order Cauchy principal value integrals
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Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type 认领 引用
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作者 Hung Viet Le 《Analysis in Theory and Applications》 CSCD 2022年第2期204-231,共28页
In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A∞.Moreover,weigh... In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A∞.Moreover,weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given. 展开更多
关键词 Commutators Muckenhoupt weights Marcinkiewicz integrals Singular integrals Sharp maximal functions BMO functions Young functions Luxemburg norm Spaces of homogeneous type
Estimates for parametric Marcinkiewicz integrals in BMOand Campanato spaces 认领 引用
19
作者 FANG Qi-quan SHI Xian-liang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第2期230-252,共23页
In this paper,the authors consider the behaviors of a class of parametricMarcinkiewicz integralsμ_Ω~ρ,μΩ,*,~ρ_λandμ_Ω~ρ,S on BMO(Rn)and Campanato spaces with com-plex parameterρand the kernelΩin Llog... In this paper,the authors consider the behaviors of a class of parametricMarcinkiewicz integralsμ_Ω~ρ,μΩ,*,~ρ_λandμ_Ω~ρ,S on BMO(Rn)and Campanato spaces with com-plex parameterρand the kernelΩin Llog~+L(Sn-1).HereμΩ,*,~ρ_λandμ_Ω~ρ,S are parametricMarcinkiewicz functions corresponding to the Littlewood-Paley g_λ~*-function and the Lusin areafunction S,respectively.Under certain weak regularity condition onΩ,the authors prove thatif f belongs to BMO(Rn)or to a certain Campanato space,then[μΩ,*,~ρ_λ(f)]~2,[μ_Ω~ρ,_S(f)]~2 and[μ_Ω~ρ(f)]~2 are either infinite everywhere or finite almost everywhere,and in the latter case,somekind of boundedness are also established. 展开更多
关键词 parametric Marcinkiewicz integrals Campanato space weak Dini-type regularity condition
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Weighted L^p-boundedness of Multilinear Oscillatory Singular Integrals with Calderón-Zygmund Kernel 认领 引用
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作者 田东风 燕敦验 《Chinese Quarterly Journal of Mathematics》 2002年第1期33-40,共8页
In this paper, weighted L p-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.
关键词 multilinear oscillatory integrals Calderón-Zygmund kernel A p-weight
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