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Fourier Transform Decay of Distributions in Hardy–Morrey Spaces

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Abstract

We establish decay estimates for Fourier transform on Hardy–Morrey spaces and its localizable version. Our work includes some aspects to these spaces linked up with pointwise Fourier estimates, in particular a natural approach on cancellation moment conditions. As application, we discuss the optimality for continuity of Fourier multipliers and pseudodifferential operators in Hardy–Morrey spaces.

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Notes

  1. The notation \(f \lesssim g \) means that there exists a constant \(C>0\) such that \(f(x)\le C g(x)\) for all \(x \in \mathbb {R}^n\).

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Acknowledgements

The authors would like to thank the referee for their careful reading and useful suggestions and comments.

Funding

This work was supported by CNPq (GrantNumber: 311321/2021-6), FAPESP (GrantNumber: 2018/15484-7).

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, São Cristóvão, SE, 49000-000, Brazil

    Marcelo F. de Almeida

  2. Departamento de Computação e Matemática, Universidade de São Paulo, Ribeirão Preto, SP, 14040-901, Brazil

    Tiago Picon

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  1. Marcelo F. de Almeida
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Correspondence to Marcelo F. de Almeida.

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The Marcelo F. de Almeida was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq - Grant 311321/2021-6). The Tiago Picon was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP - Grant 2018/15484-7).

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de Almeida, M.F., Picon, T. Fourier Transform Decay of Distributions in Hardy–Morrey Spaces. Results Math 79, 104 (2024). https://doi.org/10.1007/s00025-024-02135-1

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