In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental soluti...In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define multi-layer potentials in terms of the Poisson field and the polyharmonic fundamental solutions, in which the former is formed by the higher order conjugate Poisson and the Poisson kernels. Then by the multi-layer potentials, we solve three classes of boundary value problems(i.e., Dirichlet, Neumann and regularity problems) with L^p boundary data for polyharmonic equations in Lipschitz domains and give integral representation(or potential) solutions of these problems.展开更多
In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Planch...In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.展开更多
We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their b...We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.展开更多
Explicit Poisson kernels are found for the subelliptic Dirichlet problem with boundary data satisfying certain symmetry conditions on balls and halfspaces in some Heisenberg type groups.
We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（...We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.展开更多
We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equa...We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equation is not the dual of any standard type there exists a Kazdan-Warner type obstruction to existence of antipodal symmetry functions class.展开更多
Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation ...Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.展开更多
In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive pa...In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.展开更多
基金National Natural Science Foundation of China (Grant No. 11401254)。
文摘In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define multi-layer potentials in terms of the Poisson field and the polyharmonic fundamental solutions, in which the former is formed by the higher order conjugate Poisson and the Poisson kernels. Then by the multi-layer potentials, we solve three classes of boundary value problems(i.e., Dirichlet, Neumann and regularity problems) with L^p boundary data for polyharmonic equations in Lipschitz domains and give integral representation(or potential) solutions of these problems.
基金supported by the National Natural Science Foundation of China(11201346)
文摘In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.
基金Both authors are supported in part by the Azerbaijan-U.S. Bilateral Grants Program (project ANSF Award / 3102)The second author is also supported in part by NSF grant, DMS 0200587
文摘We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.
文摘Explicit Poisson kernels are found for the subelliptic Dirichlet problem with boundary data satisfying certain symmetry conditions on balls and halfspaces in some Heisenberg type groups.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2014JM1021)
文摘We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.
基金Supported in part by NSFC(Grant Nos.11501034 and 11571019)a key project of NSFC(Grant No.11631002)
文摘We study a prescribing involving Poisson kernel on the unit of PDE. As in Nirenberg problem, solutions. We prove existence in the functions problem of a conformally invariant integral equation ball. This integral equation is not the dual of any standard type there exists a Kazdan-Warner type obstruction to existence of antipodal symmetry functions class.
基金Supported by the Research Unit Matemática e Aplicac■s (UIMA) of University of Aveiro, Portugal
文摘Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.
基金supported by National Research Foundation of Korea (Grant No. 2011-0027230)supported in part by a grant from the Simons Foundation (Grant No. 208236)supportedin part by the MZOS Grant (Grant No. 037-0372790-2801)
文摘In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
文摘The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
基金the National Natural Science Foundation of China(No.10671022)Research Foundation for Doctor Programme (No.20060027023)Henan Institute of Education Youth Scientific Research Fund (No.20070107)
文摘In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
