Restoration of Unimodular Functions from their Holomorphic Projections

Restoration of Unimodular Functions from their Holomorphic Projections

Let P be the Bergman projection on the unit disk. Suppose that h is a real valued harmonic function and that P(eih) is in a diagonal Besov space. We show that, under appropriate a-priori constraints, we can conclude that h is in the same Besov space. Similar results are also obtained for the Hardy a...

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Veröffentlicht in:Indiana University mathematics journal 1999, Vol.48 (2), p.567-591
1. Verfasser: Rochberg, Richard
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Function spaces
Hankel operators
Harmonic functions
Inner products
Integers
Lebesgue spaces
Mathematical functions
Mathematical inequalities
Mathematics
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Zusammenfassung:Let P be the Bergman projection on the unit disk. Suppose that h is a real valued harmonic function and that P(eih) is in a diagonal Besov space. We show that, under appropriate a-priori constraints, we can conclude that h is in the same Besov space. Similar results are also obtained for the Hardy and Dirichlet projections.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.1999.48.1698