期刊
ANALYSIS & PDE
卷 3, 期 1, 页码 21-47出版社
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2010.3.21
关键词
Dirichlet space; Hankel form
资金
- Italian Minister for Research
- National Science Foundation [0070642, 0752703]
- National Science and Engineering Council of Canada
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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