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Research Article | Open Access

Characterizations of Fock-type spaces of eigenfunctions on R n

Xi Fu( ), Xiaoqiang Xie
Department of Mathematics, College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, China
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Abstract

In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on R n . As applications, we characterize Fock-type spaces of eigenfunctions on R n in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.

Keywords

eigenfunctionFock spaceLipschitz conditiondouble integral condition
CLC number: 31B05, 31B10, 30H20

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 15550-15562
DOI: 10.3934/math.2022852

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Fu X, Xie X. Characterizations of Fock-type spaces of eigenfunctions on R n . AIMS Mathematics, 2022, 7(8): 15550-15562. https://doi.org/10.3934/math.2022852

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Received: 27 March 2022
Revised: 16 June 2022
Accepted: 20 June 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)