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

Year 2023, Volume: 72 Issue: 4, 1000 - 1018, 29.12.2023

Babar Sultan , Mehvish Sultan , Ferit Gürbüz

https://doi.org/10.31801/cfsuasmas.1328691

Cited By: 5

https://izlik.org/JA46KS95RB

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

Supporting Institution

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Project Number

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Thanks

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