Journal
ANALYSIS & PDE
Volume 3, Issue 1, Pages 21-47Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2010.3.21
Keywords
Dirichlet space; Hankel form
Categories
Funding
- Italian Minister for Research
- National Science Foundation [0070642, 0752703]
- National Science and Engineering Council of Canada
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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.
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