A generalized Hilbert matrix acting on Hardy spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Chatzifountas, Christos¹  Girela, Daniel¹  Angel Pelaez, Jose¹ 

[1] Univ Malaga, Dept Anal Matemat, E-29071 Malaga, Spain

关键词: Hilbert matrices;    Hardy spaces;    BMOA;    Carleson measures;    Integration operators;    Hankel operators;    Besov spaces;    Schatten classes;   

DOI  :  10.1016/j.jmaa.2013.11.046

来源: Elsevier

【 摘 要 】

If mu is a positive Borel measure on the interval [0,1), the Hankel matrix H mu = (mu(n,k))(n,k >= 0) with entries mu n,k = integral((0, 1))t(n+k) d mu(t) induces formally the operator H mu (f) (z) = Sigma(infinity)(n=0) (Sigma(infinity)(k=0)mu(n),(a)(k)(k))z(n) on the space of all analytic functions f (z) = Sigma(infinity)(k=0) a(k)Z(k), in the unit disc ID. In this paper we describe those measures p, for which H-mu, is a bOunded (compact) operator from HP into H-q, 0 < p,q < infinity. We also characterize the measures p, for which 9-11, lies in the Schatten class S-p (H-2), 1 < p < infinity. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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