TY  - JOUR
T1  - BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand variable Herz-Morrey spaces
AU  - Gürbüz, Ferit
AU  - Sultan, Babar
AU  - Sultan, Mehvish
PY  - 2023
DA  - December
Y2  - 2023
DO  - 10.31801/cfsuasmas.1328691
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 1000
EP  - 1018
VL  - 72
IS  - 4
LA  - en
AB  - 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 $b$ isa 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 $M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$.
KW  - BMO Spaces
KW  - Marcinkiewicz integral operator
KW  - grand Herz-Morrey spaces
KW  - grand Herz spaces
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UR  - https://doi.org/10.31801/cfsuasmas.1328691
L1  - https://dergipark.org.tr/en/download/article-file/3269761
ER  -