Interpolating sequences for weighted Bergman spaces on strongly pseudoconvex bounded domains

被引:0
作者
Keshavarzi, Hamzeh [1 ]
机构
[1] Shiraz Univ, Coll Sci, Dept Math, Shiraz, Iran
关键词
Strongly pseudoconvex bounded domains; interpolating sequences; weighted Bergman spaces; CARLESON MEASURES;
D O I
10.1142/S0129167X21500269
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let 0 < p < infinity, beta > -1, and omega be a strongly pseudoconvex bounded domain with a smooth boundary in DOUBLE-STRUCK CAPITAL Cn. We will study the interpolation problem for weighted Bergman spaces A beta p(omega). In the case, 1 <= p < infinity, and beta >max{n(2p - 1) - 1,n(2q - 1) - 1}, where q is the conjugate exponent of p (let q = 1, for p = 1), we show that a sequence in & Bopf;n, the unit ball in DOUBLE-STRUCK CAPITAL Cn, is interpolating for A beta p(& Bopf; n) if and only if it is separated.
引用
收藏
页数:14
相关论文
共 19 条
  • [1] Abate M., 1989, Iteration Theory of Holomorphic Maps on Taut Manifolds. Research and Lecture Notes in Mathematics. Complex Analysis and Geometry
  • [2] Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains
    Abate, Marco
    Saracco, Alberto
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2011, 83 : 587 - 605
  • [3] BERNDTSSON B, 1985, P K NED AKAD A MATH, V88, P1
  • [4] AN INTERPOLATION PROBLEM FOR BOUNDED ANALYTIC FUNCTIONS
    CARLESON, L
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1958, 80 (04) : 921 - 930
  • [5] INTERPOLATIONS BY BOUNDED ANALYTIC FUNCTIONS AND CORONA PROBLEM
    CARLESON, L
    [J]. ANNALS OF MATHEMATICS, 1962, 76 (03) : 547 - &
  • [6] Cowen C., 1995, Composition Operators on Spaces of Analytic Functions
  • [7] DUREN P., 2004, Bergman spaces, V100
  • [8] Hedenmalm H., 2000, Theory of Bergman Spaces, DOI DOI 10.1007/978-1-4612-0497-8
  • [9] Carleson measures and balayage for Bergman spaces of strongly pseudoconvex domains
    Hu, Zhangjian
    Lv, Xiaofen
    Zhu, Kehe
    [J]. MATHEMATISCHE NACHRICHTEN, 2016, 289 (10) : 1237 - 1254
  • [10] Jevtic M, 1996, MICH MATH J, V43, P495