Matches in SemOpenAlex for { <https://semopenalex.org/work/W3124653795> ?p ?o ?g. }
- W3124653795 abstract "Let $X$ be a ball Banach function space on ${mathbb R}^n$. Let $Omega$ be a Lipschitz function on the unit sphere of ${mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_Omega$ be the convolutional singular integral operator with kernel $Omega(cdot)/|cdot|^n$. In this article, under the assumption that the Hardy--Littlewood maximal operator $mathcal{M}$ is bounded on both $X$ and its associated space, the authors prove that the commutator $[b,T_Omega]$ is compact on $X$ if and only if $bin{rm CMO}({mathbb R}^n)$. To achieve this, the authors mainly employ three key tools: some elaborate estimates, given in this article, on the norm in $X$ of the commutators and the characteristic functions of some measurable subset,which are implied by the assumed boundedness of ${mathcal M}$ on $X$ and its associated space as well as the geometry of $mathbb R^n$; the complete John--Nirenberg inequality in $X$ obtained by Y. Sawano et al.; the generalized Fr'{e}chet--Kolmogorov theorem on $X$ also established in this article. All these results have a wide range of applications. Particularly, even when $X:=L^{p(cdot)}({mathbb R}^n)$ (the variable Lebesgue space), $X:=L^{vec{p}}({mathbb R}^n)$ (the mixed-norm Lebesgue space), $X:=L^Phi({mathbb R}^n)$ (the Orlicz space), and $X:=(E_Phi^q)_t({mathbb R}^n)$ (the Orlicz-slice space or the generalized amalgam space), all these results are new." @default.
- W3124653795 created "2021-02-01" @default.
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- W3124653795 date "2021-01-18" @default.
- W3124653795 modified "2023-10-17" @default.
- W3124653795 title "Compactness Characterizations of Commutators on Ball Banach Function Spaces" @default.
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- W3124653795 doi "https://doi.org/10.48550/arxiv.2101.07407" @default.
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