BILINEAR FORMS ON THE DIRICHLET SPACE

被引：32

作者：

Arcozzi, Nicola ^{[1
]}

Rochberg, Richard ^{[2
]}

Sawyer, Eric ^{[3
]}

Wick, Brett D. ^{[4
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, I-40127 Bologna, Italy

[2] Washington Univ, Dept Math, St Louis, MO 63130 USA

[3] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

[4] Univ S Carolina, Dept Math, LeConte Coll, Columbia, SC 29208 USA

来源：

ANALYSIS & PDE | 2010年 / 3卷 / 01期

基金：

美国国家科学基金会;

关键词：

Dirichlet space; Hankel form;

D O I：

10.2140/apde.2010.3.21

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the bilinear form B-b(f, g) = < f g, b > is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if vertical bar b'vertical bar(2) dx dy is a Carleson measure for the Dirichlet space. This is completely analogous to the results for boundedness of Hankel forms on the Hardy and Bergman spaces, but the proof is quite different, relying heavily on potential-theoretic constructions.

引用

页码：21 / 47

页数：27

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