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Study of twisted Bargmann transform via Bargmann transform

Shubham R. Bais and Venku Naidu D
From the journal Forum Mathematicum

Abstract

In the present article, we give an alternate and easier proof for the image characterization of L2(2n) under the twisted Bargmann transform which was earlier studied by Krontz, Thangavelu and Xu. As a consequence, we study some properties of the twisted Bergman spaces for 0<p and the Lp-boundedness of the twisted Bargmann transform, 1p. We also study Lp-boundedness of the twisted Bargmann projection Pt and the duality relations between the spaces Btp(2n), 1<p<.

MSC 2010: 30H20; 45P05; 46B10

Communicated by Christopher D. Sogge


Funding statement: The first author thanks the University Grant Commission (UGC) for providing financial support.

Acknowledgements

We thank the referee for meticulously reading our manuscript and giving us several valuable suggestions in revising the manuscript.

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Received: 2021-05-08
Revised: 2021-10-07
Published Online: 2021-10-23
Published in Print: 2021-11-01

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