The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponents

Yin Liu; Lushun Wang

doi:10.4134/BKMS.b230224

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(2): 529-540

Online first article March 12, 2024 Printed March 31, 2024

https://doi.org/10.4134/BKMS.b230224

The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponents

Yin Liu, Lushun Wang

Nanyang Normal University; Zhejiang Normal University

Abstract

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Abstract

In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear H\"{o}rmander class $BS_{1,1}^m$ in variable Triebel-Lizorkin spaces and variable Besov spaces.

Keywords: Bilinear pseudodifferential operators, variable exponent, Besov spaces, Triebel-Lizorkin spaces

MSC numbers: Primary 47G30, 42B35, 42B25

Supported by: Y.~Liu is supported by the Tianyuan foundation for mathematics of the National Natural Science Foundation of China (No.~12126342), the Natural Science Foundation of Henan Province (No.~202300410300) and the Youth Program of Nanyang Normal University (No.~2024QN014). L.~Wang is financially supported by the National Natural Science Foundation of China (No.~11901531) and China Scholarship Council (No.~202008330417).