Normal weighted Bergman type operators on mixed norm spaces over the ball in $\mathbb C^n$

Karen L. Avetisyan; Albert I. Petrosyan

doi:10.4134/JKMS.j170195

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2018; 55(2): 313-326

Online first article February 5, 2018 Printed March 1, 2018

https://doi.org/10.4134/JKMS.j170195

Normal weighted Bergman type operators on mixed norm spaces over the ball in $\mathbb C^n$

Karen L. Avetisyan, Albert I. Petrosyan

Yerevan State University, Yerevan State University

Abstract

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Abstract

The paper studies some new $\mathbb C^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter $\beta$ for which these operators are bounded on mixed norm spaces $L(p,q,\beta)$ over the unit ball in $\mathbb C^n$. Moreover, these operators are bounded projections as well, and the images of $L(p,q,\beta)$ under the projections are found.

Keywords: normal weight, mixed norm space, Bergman operator

MSC numbers: Primary 47B38, 32A37