Bilinear Forms on The Dirichlet Space

Nicola Arcozzi; Richard Rochberg; Eric Sawyer; Brett D. Wick

doi:10.2140/apde.2010.3.21

Bilinear Forms on The Dirichlet Space

Nicola Arcozzi
, Richard Rochberg
, Eric Sawyer
, Brett D. Wick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We show that the bilinear form (Equation Presented) is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if |b0|´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.

Original language	English
Pages (from-to)	21-47
Number of pages	27
Journal	Analysis and PDE
Volume	3
Issue number	1
DOIs	https://doi.org/10.2140/apde.2010.3.21
State	Published - 2010

Keywords

Dirichlet space
Hankel form

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10.2140/apde.2010.3.21

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title = "Bilinear Forms on The Dirichlet Space",

abstract = "We show that the bilinear form (Equation Presented) is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if |b0|´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.",

keywords = "Dirichlet space, Hankel form",

author = "Nicola Arcozzi and Richard Rochberg and Eric Sawyer and Wick, \{Brett D.\}",

note = "Publisher Copyright: {\textcopyright} 2010 by Mathematical Sciences Publishers",

year = "2010",

doi = "10.2140/apde.2010.3.21",

language = "English",

volume = "3",

pages = "21--47",

journal = "Analysis and PDE",

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T1 - Bilinear Forms on The Dirichlet Space

AU - Arcozzi, Nicola

AU - Rochberg, Richard

AU - Sawyer, Eric

AU - Wick, Brett D.

PY - 2010

Y1 - 2010

N2 - We show that the bilinear form (Equation Presented) is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if |b0|´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.

AB - We show that the bilinear form (Equation Presented) is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if |b0|´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.

KW - Dirichlet space

KW - Hankel form

UR - https://www.scopus.com/pages/publications/78649887382

U2 - 10.2140/apde.2010.3.21

DO - 10.2140/apde.2010.3.21

M3 - Article

AN - SCOPUS:78649887382

SN - 2157-5045

VL - 3

SP - 21

EP - 47

JO - Analysis and PDE

JF - Analysis and PDE

IS - 1

ER -

Bilinear Forms on The Dirichlet Space

Abstract

Keywords

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