@article{AlNemer2025, 
author = {Ghada AlNemer and Ghada Ali Basendwah and Mehvish Sultan and Ioan-Lucian Popa},
title = {Generalizations of Herz-Morrey spaces and boundedness of the Calderón-Zygmund operators},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {17403-17422},
keywords = {multilinear Calderón-Zygmund operators, grand Herz-Morrey spaces, grand Herz spaces},
url = {https://www.sciopen.com/article/10.3934/math.2025778},
doi = {10.3934/math.2025778},
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      (      ⋅      )        (            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.}
}