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Main Author: Chen, You-Wei Benson
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.16707
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author Chen, You-Wei Benson
author_facet Chen, You-Wei Benson
contents In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_αf \in BMO(\mathbb{R}^n) \text{ if and only if } I_αf \in BMO^β(\mathbb{R}^n) \text{ for } β\in (n-α,n]. \end{align*} Here $I_α$ denotes the Riesz potential of order $α$ and $BMO^β$ represents the space of functions of bounded $β$-dimensional mean oscillation.
format Preprint
id arxiv_https___arxiv_org_abs_2404_16707
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A self-improving property of Riesz potentials in BMO
Chen, You-Wei Benson
Functional Analysis
In this paper we prove that for non-negative measurable functions $f$, \begin{align*} I_αf \in BMO(\mathbb{R}^n) \text{ if and only if } I_αf \in BMO^β(\mathbb{R}^n) \text{ for } β\in (n-α,n]. \end{align*} Here $I_α$ denotes the Riesz potential of order $α$ and $BMO^β$ represents the space of functions of bounded $β$-dimensional mean oscillation.
title A self-improving property of Riesz potentials in BMO
topic Functional Analysis
url https://arxiv.org/abs/2404.16707