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
Copyright © The Korean Mathematical Society.
Yin Liu, Lushun Wang
Nanyang Normal University; Zhejiang Normal University
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).
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