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Real Hardy Space, Multidimensional Variations, and Integrability of the Fourier Transform

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Abstract

A new class of functions is introduced closely related to that of functions with bounded Tonelli variation and to the real Hardy space. For this class, conditions for integrability of the Fourier transform are established.

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Acknowledgements

The first and the third author are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and they are partially supported by the “Department of Mathematics and Computer Science” of the University of Perugia (Italy) within the project “Metodi di Teoria dell’Approssimazione, Analisi Reale, Analisi Nonlineare e loro applicazioni”.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Universita’ degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    L. Angeloni & G. Vinti

  2. Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel

    E. Liflyand

  3. Regional Mathematical Center of Southern Federal University, Bolshaya Sadovaya Str. 105/42, Rostov-on-Don, Russia, 344006

    E. Liflyand

Authors
  1. L. Angeloni
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  2. E. Liflyand
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  3. G. Vinti
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Correspondence to E. Liflyand.

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Communicated by Irene Sabadini.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Angeloni, L., Liflyand, E. & Vinti, G. Real Hardy Space, Multidimensional Variations, and Integrability of the Fourier Transform. Complex Anal. Oper. Theory 14, 64 (2020). https://doi.org/10.1007/s11785-020-01021-2

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  • DOI: https://doi.org/10.1007/s11785-020-01021-2

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