The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decompos...The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderon-Zygmund operators on these Hardy spaces are studied.展开更多
Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥...Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D^2.展开更多
基金Project (19871071) supported by National Natural Science Foundation of China
文摘The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderon-Zygmund operators on these Hardy spaces are studied.
基金Supported by NSFC(Grant Nos.11271332 and 11431011)the Fundamental Research Funds for the Central UniversitiesNSFC(Grant No.11501249)
文摘Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D^2.
基金Project 10871003 supported-by National Natural Science Foundation of Chinathe Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20030001107)
文摘In this paper, we prove Beurling＇s theorem for the Jacobi transform, from which we derive some other versions of uncertainty principles.
文摘对于实轴上满足M条件的自同胚映射h(x),利用一系列积分不等式的精细估计,将相应问题转化为定义在一个凸五边形约束域G上伸张函数f(ξ,η)的估计式;然后根据f(ξ,η)的凸性和其在区域G 5个顶点上函数值的直接计算,从而得到了Beurling-A h lfors扩张映射φ(z)的伸张函数D的最优值估计:D≤2M.本文的证明不同于Lehtinen传统方法.
