By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels...By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.展开更多
In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size condi...In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.展开更多
We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhard...We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.展开更多
Some estimates for the convolution operators with kernels of type （l, r） on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established.
基金Supported by Guangdong Basic and Applied Basic Research Foundation Natural Science Foundation(Grant No.2021A1515010055)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.
基金Supported by the National Natural Science Foundation of China(12071437)the Natural Science Foundation of Zhejiang Province,China(LQ22A010018)。
文摘In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.
基金supported by the National Natural Science Foundation of China(11371257)Colleges and Universities Science and Technology Research Foundation of Hebei Province(QN2016304)
文摘We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.
基金Project 10261007 supported by NSFC.supported by SF of Xinjiang University
文摘Some estimates for the convolution operators with kernels of type （l, r） on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established.
