Positive kernel functions and Bergman spaces. (English) Zbl 0659.32010
Using the positive (“Poisson-like”) reproducing kernel for the weighted Bergman spaces \(A^{p,\delta}({\mathbb{B}})\), the author obtains Hardy- Littlewood inequalities for functions in these spaces. Similar results are obtained in the setting of the generalized half plane in \({\mathbb{C}}^ n\). As an application, the author treats the Mackey topology on \(A^{p,\delta}({\mathbb{B}})\), \(0<p<1\) and extends a one variable result due to J. Shapiro [Duke Math. J. 43, 187-202 (1976; Zbl 0354.46036)].
Reviewer: E.Straube
MSC:
| 32A35 | \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables |
| 46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |
Citations:
Zbl 0354.46036References:
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