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Bilinear forms on the
Dirichlet space
Nicola Arcozzi, Richard Rochberg, Eric Sawyer and Brett D. Wick |
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Vol. 3 (2010), No. 1, 21–47
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Abstract |
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We show that the bilinear form is bounded on the Dirichlet space of holomorphic functions on the unit disk if and only if 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
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Mathematical Subject Classification 2000
Primary: 30C85, 47B35, 31C25
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Milestones
Received: 8 July 2009
Revised: 99 2999
Accepted: 5 August 2009
Published: 4 March 2010
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Authors |
| Nicola Arcozzi | |
| Dipartimento di Matematica Università di Bologna 40127 Bologna Italy |
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| Richard Rochberg | |
| Department of Mathematics Washington University St. Louis, MO 63130 United States |
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| Eric Sawyer | |
| Department of Mathematics and
Statistics McMaster University Hamilton, ON L8S 4K1 Canada |
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| Brett D. Wick | |
| Department of Mathematics LeConte College 1523 Greene Street University of South Carolina Columbia, SC 29208 United States |
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