BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand variable Herz-Morrey spaces

Authors : Babar Sultan, Mehvish Sultan, Ferit Gürbüz

Pages : 1000-1018

Doi:10.31801/cfsuasmas.1328691

View : 108 | Download : 88

Publication Date : 2023-12-29

Article Type : Research Paper

Abstract :Let $\\mathbb{S}^{n-1}$ denote the unit sphere in $\\mathbb{R}^n$ with the normalized Lebesgue measure. Let $\\Phi\\in L^{r}(\\mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $\\mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,\\mu_{\\Phi}]^m$ and prove the boundedness of $[b,\\mu_{\\Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $M\\dot{K}^{\\alpha(.),\\beta}_{u,v(.)}(\\mathbb{R}^n)$.
Keywords : BMO Spaces, Marcinkiewicz integral operator, grand Herz Morrey spaces, grand Herz spaces