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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sharp estimate for $ A\sp p\sb \alpha$ functions in $ {\bf C}\sp n$


Author: Dragan Vukotić
Journal: Proc. Amer. Math. Soc. 117 (1993), 753-756
MSC: Primary 46E15; Secondary 30H05, 46J15
MathSciNet review: 1120512
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Abstract: We observe that involutive automorphisms $ {\varphi _a}$ of the unit ball in $ {{\mathbf{C}}^n}$ induce surjective involutive isometries of the weighted Bergman space $ A_\alpha ^p(0 < p < \infty ,\;\alpha > - 1)$. By means of these isometries we solve an extremal problem for the point-evaluation functional, thus obtaining a sharp estimate for $ \vert f(z)\vert$ in terms of $ \vert\vert f\vert{\vert _{p,\alpha }}$ and $ \vert z\vert$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1120512-1
PII: S 0002-9939(1993)1120512-1
Keywords: Weighted Bergman space, extremal problem, involutive isometries, point-evaluation functional
Article copyright: © Copyright 1993 American Mathematical Society