June 2023 BILINEAR θ-TYPE GENERALIZED FRACTIONAL INTEGRAL AND ITS COMMUTATOR ON NONHOMOGENEOUS METRIC MEASURE SPACES
Guanghui Lu, Shuangping Tao
Rocky Mountain J. Math. 53(3): 839-857 (June 2023). DOI: 10.1216/rmj.2023.53.839

Abstract

We establish the boundedness of the bilinear 𝜃-type generalized fractional integral and its commutator on nonhomogeneous metric measure space. Under the assumption that the functions Φ and λ satisfy certain conditions, we prove that the bilinear 𝜃-type generalized fractional integral BT~𝜃,α is bounded from the product of generalized Morrey spaces p1,Φ,κ(μ)×p2,Φ,κ(μ) into spaces q,Φqp,κ(μ), and it is also bounded from the product of spaces p1,Φ,κ(μ)×p2,Φ,κ(μ) into generalized weak Morrey spaces W1,Φ1p,κ(μ). Furthermore, the boundedness of the commutator [b1,b2,BT~𝜃,α] formed by b1,b2RBMO ~(μ) and BT~𝜃,α on spaces q,Φqp,κ(μ) and on spaces W1,Φ1p,κ(μ) is also obtained.

Citation

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Guanghui Lu. Shuangping Tao. "BILINEAR θ-TYPE GENERALIZED FRACTIONAL INTEGRAL AND ITS COMMUTATOR ON NONHOMOGENEOUS METRIC MEASURE SPACES." Rocky Mountain J. Math. 53 (3) 839 - 857, June 2023. https://doi.org/10.1216/rmj.2023.53.839

Information

Received: 16 March 2022; Revised: 26 July 2022; Accepted: 26 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617915
zbMATH: 07731149
Digital Object Identifier: 10.1216/rmj.2023.53.839

Subjects:
Primary: 42B20
Secondary: 30L99 , 42B35

Keywords: bilinear 𝜃-type , commutator , generalized fractional integral , generalized Morrey space , nonhomogeneous metric measure spaces

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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