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$\boldsymbol {L^{p}}$ REGULARITY OF THE SZEGÖ PROJECTION ON THE SYMMETRISED POLYDISC

Part of: Harmonic analysis in several variables Holomorphic functions of several complex variables

Published online by Cambridge University Press:  12 May 2022

KAIKAI HAN Open the ORCID record for KAIKAI HAN [Opens in a new window]  and
YANYAN TANG Open the ORCID record for YANYAN TANG [Opens in a new window]
KAIKAI HAN
Affiliation:
School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, PR China e-mail: [email protected]
YANYAN TANG*
Affiliation:
School of Mathematics and Statistics, Henan University, Kaifeng 475000, PR China
*
e-mail: [email protected]
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Abstract

We consider the $L^{p}$ -regularity of the Szegö projection on the symmetrised polydisc $\mathbb {G}_{n}$ . In the setting of the Hardy space corresponding to the distinguished boundary of the symmetrised polydisc, it is shown that this operator is $L^{p}$ -bounded for $p\in (2-{1}/{n}, 2+{1}/{(n-1)})$ .

Keywords

L p-regularitysymmetrised polydiscSzegö projection

MSC classification

Primary: 32A36: Bergman spaces
Secondary: 32A25: Integral representations; canonical kernels (Szegő, Bergman, etc.) 42B30: $H^p$-spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 481 - 490
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

K.H. is supported by the National Natural Science Foundation of China (Grant No. 12101179) and Scientific Research and Development Program of Hebei University of Economics and Business, PR China (2021QN01). Y.T. is supported by the National Natural Science Foundation of China (Grant No. 12101185).

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