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2010 Bilinear forms on the Dirichlet space
Nicola Arcozzi, Richard Rochberg, Eric Sawyer, Brett Wick
Anal. PDE 3(1): 21-47 (2010). DOI: 10.2140/apde.2010.3.21

Abstract

We show that the bilinear form Bb(f,g)=fg,b is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if |b|2dxdy 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.

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Nicola Arcozzi. Richard Rochberg. Eric Sawyer. Brett Wick. "Bilinear forms on the Dirichlet space." Anal. PDE 3 (1) 21 - 47, 2010. https://doi.org/10.2140/apde.2010.3.21

Information

Received: 8 July 2009; Accepted: 5 August 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1262.30066
MathSciNet: MR2663410
Digital Object Identifier: 10.2140/apde.2010.3.21

Subjects:
Primary: 30C85, 31C25, 47B35

Rights: Copyright © 2010 Mathematical Sciences Publishers

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