Open Access
Translator Disclaimer
August, 2022 The $L^p$-$L^q$ Boundedness and Compactness of Bergman Type Operators
Lijia Ding, Kai Wang
Author Affiliations +
Taiwanese J. Math. 26(4): 713-740 (August, 2022). DOI: 10.11650/tjm/220101

Abstract

We investigate Bergman type operators on the complex unit ball, which are singular integral operators induced by the modified Bergman kernel. We consider the $L^p$-$L^q$ boundedness and compactness of Bergman type operators. The results of boundedness can be viewed as the Hardy–Littlewood–Sobolev (HLS) type theorem in the case unit ball. We also give some sharp norm estimates of Bergman type operators which in fact gives the upper bounds of the optimal constants in the HLS type inequality on the unit ball. Moreover, a trace formula is given.

Funding Statement

The first author was partially supported by PCPSF (2020M680172, 2020T130016). The second author was partially supported by NSFC (12026250, 11722102) and STIP (21JC1400800).

Acknowledgments

The first author would like to thank Professor Genkai Zhang for his helpful discussions and warm hospitality when the author visited Chalmers University of Technology. The first author gratefully acknowledges the many suggestions of Professor Zipeng Wang. The authors would like to thank Professor H. Kaptanoğlu devoutly for sending us their recent work.

Citation

Download Citation

Lijia Ding. Kai Wang. "The $L^p$-$L^q$ Boundedness and Compactness of Bergman Type Operators." Taiwanese J. Math. 26 (4) 713 - 740, August, 2022. https://doi.org/10.11650/tjm/220101

Information

Received: 9 September 2021; Revised: 29 December 2021; Accepted: 2 January 2022; Published: August, 2022
First available in Project Euclid: 9 January 2022

Digital Object Identifier: 10.11650/tjm/220101

Subjects:
Primary: 47G10
Secondary: 47A30 , 47B07

Keywords: Bergman projection , Compact operator , Embedding theorem , Hardy–Littlewood–Sobolev theorem , norm estimate

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.26 • No. 4 • August, 2022
Back to Top