Weighted local Hardy spaces with variable exponents

Mitsuo Izuki, Toru Nogayama, Takahiro Noi and Yoshihiro Sawano

Mathematische Nachrichten, 2023, vol. 296, issue 12, 5710-5785

Abstract: This paper defines local weighted Hardy spaces with variable exponents. 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 applications, we obtain the boundedness of singular integral operators, the Littlewood–Paley characterization, and wavelet decomposition.

Date: 2023
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https://doi.org/10.1002/mana.202200248

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