AIMS Mathematics (Jan 2022)

Weighted and endpoint estimates for commutators of bilinear pseudo-differential operators

  • Yanqi Yang,
  • Shuangping Tao,
  • Guanghui Lu

DOI
https://doi.org/10.3934/math.2022333
Journal volume & issue
Vol. 7, no. 4
pp. 5971 – 5990

Abstract

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In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function. By establishing the pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained respectively on the products of weighted Lebesgue spaces and variable exponent Lebesgue spaces with $ \sigma \in\mathcal{B}BS_{1, 1}^{1} $. Moreover, the endpoint estimate of the commutators is also established on $ L^{\infty}\times L^{\infty} $.

Keywords