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February 2022 Boundedness of certain bilinear operators on vanishing generalized Morrey spaces
Mengfei Luo, Xing Fu
Rocky Mountain J. Math. 52(1): 223-242 (February 2022). DOI: 10.1216/rmj.2022.52.223

Abstract

In this article, we consider the bilinear operator T satisfying that there exists a positive constant C(T), depending on T, such that, for any measurable functions f and g with compact support, t with 0<|t|1, and xn with 0supp(f(xt))supp(g(x)),

T(f,g)(x)C(T)nf(xty)g(xy)|y|ndy.

We investigate the boundedness of T on the vanishing generalized Morrey spaces V0Lp,φ(n) and VLp,φ(n), and the boundedness of the subbilinear maximal operator on the vanishing generalized Morrey space V()Lp,φ(n), and their applications to some classical (sub)bilinear operators in harmonic analysis. As a byproduct, we also show that T is bounded on generalized Morrey spaces Lp,φ(n). Some typical examples for the main results of this paper are also included.

Citation

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Mengfei Luo. Xing Fu. "Boundedness of certain bilinear operators on vanishing generalized Morrey spaces." Rocky Mountain J. Math. 52 (1) 223 - 242, February 2022. https://doi.org/10.1216/rmj.2022.52.223

Information

Received: 9 October 2020; Accepted: 1 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.223

Subjects:
Primary: 42B20
Secondary: 42B25 , 42B35 , 47A07

Keywords: bilinear operators , boundedness , vanishing generalized Morrey spaces

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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