Composition of rough singular integral operators on rearrangement invariant Banach type spaces

Fuente: arXiv
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Main Authors: Tan, Jiawei, Xue, Qingying
Format: Preprint
Published: 2024
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author Tan, Jiawei
Xue, Qingying
author_facet Tan, Jiawei
Xue, Qingying
contents Let $Ω$ be a homogeneous function of degree zero and enjoy the vanishing condition on the unit sphere $\mathbb{S}^{n-1}(n\geq 2)$. Let $T_Ω$ be the convolution singular integral operator with kernel ${Ω(x)}{|x|^{-n}}$. In this paper, when $Ω\in L^{\infty}(\mathbb {S}^{n-1})$, we consider the quantitative weighted bounds of the composite operators of $T_Ω$ on rearrangement invariant Banach function spaces. These spaces contain the classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces were also given.
format Preprint
id arxiv_https___arxiv_org_abs_2403_05840
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Composition of rough singular integral operators on rearrangement invariant Banach type spaces
Tan, Jiawei
Xue, Qingying
Classical Analysis and ODEs
42B20
Let $Ω$ be a homogeneous function of degree zero and enjoy the vanishing condition on the unit sphere $\mathbb{S}^{n-1}(n\geq 2)$. Let $T_Ω$ be the convolution singular integral operator with kernel ${Ω(x)}{|x|^{-n}}$. In this paper, when $Ω\in L^{\infty}(\mathbb {S}^{n-1})$, we consider the quantitative weighted bounds of the composite operators of $T_Ω$ on rearrangement invariant Banach function spaces. These spaces contain the classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces were also given.
title Composition of rough singular integral operators on rearrangement invariant Banach type spaces
topic Classical Analysis and ODEs
42B20
url https://arxiv.org/abs/2403.05840