HILBERT MATRIX OPERATOR ON SPACES OF ANALYTIC FUNCTIONS

被引：20

作者：

Lanucha, Bartosz ^{[1
]}

Nowak, Maria ^{[1
]}

Pavlovic, Miroslav ^{[2
]}

机构：

[1] Uniwersytet Marii Curie Sklodowskiej Lublinie, Inst Matemat, PL-20031 Lublin, Poland

[2] Univ Beogradu, Matemat Fak, Belgrade 11001, Serbia

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2012年 / 37卷 / 01期

关键词：

Hilbert matrix; Hardy spaces; Bergman spaces; Bloch and Besov spaces; BERGMAN;

D O I：

10.5186/aasfm.2012.3715

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the action of the Hilbert matrix operator, H, On the Hardy space H-1, weighted Hardy spaces H-alpha(p) (alpha >= 0), Bergman spaces with logarithmic weights, etc. In particular, we extend Diamantopoulos-Siskakis result by proving that H maps H-alpha(p) into H-alpha(p) if and only if alpha+1/p < 1. A criterion for Hf to belong to H-1 is given provided the coefficients of f are nonnegative. Also, H maps the A(2)-space with weight log(alpha)(2/(1 - vertical bar z vertical bar(2))) into the ordinary Bergman space A(2) if alpha > 3. Similarly, the Bloch space with logarithmic weight is mapped by H into the ordinary Bloch space.

引用

页码：161 / 174

页数：14