An Application of the Pr\'ekopa-Leindler Inequality and Sobolev Regularity of Weighted Bergman Projections
Yunus E. Zeytuncu
TL;DR
This paper establishes Sobolev estimates for weighted Bergman projections on convex Reinhardt domains by leveraging the Prékopa-Leindler inequality, extending previous results in complex analysis.
Contribution
It introduces a general version of a known theorem to derive Sobolev estimates for weighted Bergman projections using the Prékopa-Leindler inequality.
Findings
Sobolev estimates for weighted Bergman projections on convex Reinhardt domains
Extension of a classical theorem to a broader setting
Application of the Prékopa-Leindler inequality in complex analysis
Abstract
We prove a general version of \cite[Theorem 4.1]{Boas84} to obtain Sobolev estimates for weighted Bergman projections on convex Reinhardt domains by using the Pr\'ekopa-Leindler inequality.
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