Weighted local Hardy spaces with variable exponents

2022/06/12 by Mitsuo Izuki, Izuki, Mitsuo, Toru Nogayama +5
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2206.05674

openalex publication_date 2022/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the functions in the Lebesgue spaces with exponentially decaying exponent. As an application, we obtain the boundedness of singular integral operators, the Littlewood--Paley characterization and wavelet decomposition.

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