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- W4291960846 abstract "Let $X$ be a ball quasi-Banach function space on ${mathbb R}^n$ satisfying some mild assumptions. In this article, the authors first find a reasonable version $widetilde{T}$ of the Calder'on--Zygmund operator $T$ on the ball Campanato-type function space $mathcal{L}_{X,q,s,d}(mathbb{R}^n)$ with $qin[1,infty)$, $sinmathbb{Z}_+^n$, and $din(0,infty)$. Then the authors prove that $widetilde{T}$ is bounded on $mathcal{L}_{X,q,s,d}(mathbb{R}^n)$ if and only if, for any $gammainmathbb{Z}^n_+$ with $|gamma|leq s$, $T^*(x^{gamma})=0$, which is hence sharp. Moreover, $widetilde{T}$ is proved to be the adjoint operator of $T$, which further strengthens the rationality of the definition of $widetilde{T}$. All these results have a wide range of applications. In particular, even when they are applied, respectively, to weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces, Orlicz-slice spaces, Morrey spaces, mixed-norm Lebesgue spaces, local generalized Herz spaces, and mixed-norm Herz spaces, all the obtained results are new. The proofs of these results strongly depend on the properties of the kernel of $T$ under consideration and also on the dual theorem on $mathcal{L}_{X,q,s,d}(mathbb{R}^n)$." @default.
- W4291960846 created "2022-08-16" @default.
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- W4291960846 date "2022-08-12" @default.
- W4291960846 modified "2023-09-24" @default.
- W4291960846 title "Boundedness of Calder'on--Zygmund operators on ball Campanato-type function spaces" @default.
- W4291960846 doi "https://doi.org/10.48550/arxiv.2208.06266" @default.
- W4291960846 hasPublicationYear "2022" @default.
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