A new characterization of Bergman–Schatten spaces and a duality result

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• 作者：L.G. Marcoci ; L.E. Persson ; I. Popa ; N. Popa
• 关键词：Infinite matrices ; Toeplitz matrices ; Schur multipliers ; Bergman&#x2013 ; Schatten spaces ; Bloch spaces ; Duality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2009
• 出版时间：1 December 2009
• 年：2009
• 卷：360
• 期：1
• 页码：67-80
• 全文大小：252 K

文摘

Let denote the space of all upper triangular matrices A such that lim_r→1⁻(1−r²)(A*C(r))^′_B(ℓ²)=0. We also denote by the closed Banach subspace of consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between and the Bergman&#x2013;Schatten spaces . We also give a characterization of the more general Bergman&#x2013;Schatten spaces , 1p<∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, L^p-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219&#x2013;237] for classical Bergman spaces.