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http://dx.doi.org/10.4134/BKMS.b210839

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1471-1493 More about this Journal
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
Bilinear Calderon-Zygmund operator; commutator; space BMO; Lipschitz space; generalized variable exponent Morrey space;
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