Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ESTIMATE FOR BILINEAR CALDERÓN-ZYGMUND OPERATOR AND ITS COMMUTATOR ON PRODUCT OF VARIABLE EXPONENT SPACES

  • Guanghui, Lu (College of Mathematics and Statistics Northwest Normal University) ;
  • Shuangping, Tao (College of Mathematics and Statistics Northwest Normal University)
  • Received : 2021.11.20
  • Accepted : 2022.06.15
  • Published : 2022.11.30
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Abstract

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b1, b2, BT] which is generated by b1, b2 ∈ BMO(ℝn) (or ${\dot{\Lambda}}_{\alpha}$(ℝn)) and the BT on generalized variable exponent Morrey spaces 𝓛p(·),𝜑(ℝn). Under assumption that the functions 𝜑1 and 𝜑2 satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛p1(·),𝜑1(ℝn)×𝓛p2(·),𝜑2(ℝn) into space 𝓛p(·),𝜑(ℝn). Furthermore, the boundedness of commutator [b1, b2, BT] on spaces Lp(·)(ℝn) and on spaces 𝓛p(·),𝜑(ℝn) is also established.

Keywords

Acknowledgement

This work was financially supported by Young Teachers' Scientific Research Ability Promotion Project of Northwest Normal University (NWNU-LKQN2020-07), Innovation Fund Project for Higher Education of Gansu Province (2020A-010) and NNSF(11561062).

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