Work

Generalizations of Herz-Morrey spaces and boundedness of the Calderón-Zygmund operators

Year: 2025

Type: article

Abstract: In this paper, we use the grand variable Herz-Morrey spaces, and our main objective is to prove the boundedness of multilinear Calderón-Zygmund operators on the product of grand variable Herz-Morrey spaces. We first define the Lebesgue spaces with variable exponents and some basic lemmas including Hölder's inequality for Lebesgue spaces. To prove the boundedness of multilinear Calderón-Zygmund operators on grand variable Herz-Morrey spaces, we use the well known Hölder's inequality and Minkonwski's inequality. We split the summation of grand variable Herz-Morrey spaces to find the $ L^{p(\cdot)}(\mathbb{R}^n) $ estimate of the characteristic function under some conditions. After finding estimate of each term, we conclude that multilinear Calderón-Zygmund operators are bounded on grand variable Herz-Morrey spaces. Our results generalize some results on variable Herz spaces and grand variable Herz spaces.

Source: AIMS Mathematics

DOI: 10.3934/math.2025778

Authors: Ghada AlNemer, Ghada Ali Basendwah, Mehvish Sultan, Ioan-Lucian Popa

Institutions: Princess Nourah bint Abdulrahman University, King Abdulaziz University, Capital University of Science and Technology, Transylvania University of Brașov

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Princess Nourah Bint Abdulrahman University