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$ L^p$ mapping properties of the Bergman projection on the Hartogs triangle

Authors: Debraj Chakrabarti and Yunus E. Zeytuncu
Journal: Proc. Amer. Math. Soc. 144 (2016), 1643-1653
MSC (2010): Primary 32A25, 32A07
Published electronically: August 12, 2015
MathSciNet review: 3451240
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Abstract: We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted $ L^p$ spaces when $ p>\frac {4}{3}$, where the weight is a power of the distance to the singular boundary point. For $ 1<p\leq \frac {4}{3}$ we show that no such weighted estimates are possible.

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Additional Information

Debraj Chakrabarti
Affiliation: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859

Yunus E. Zeytuncu
Affiliation: Department of Mathematics and Statistics, University of Michigan - Dearborn, Dearborn, Michigan 48128

Keywords: Bergman projection, Hartogs triangle, $L^p$ regularity
Received by editor(s): December 12, 2014
Received by editor(s) in revised form: April 28, 2015
Published electronically: August 12, 2015
Additional Notes: The first author was partially supported by grant #316632 from the Simons Foundation and also by an Early Career internal grant from Central Michigan University
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society

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