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On Hardy and Bellman transforms of the Fourier coefficients of functions in symmetric spaces

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Abstract

The author finds sufficient conditions for invariance of a symmetric function space under the Hardy and Bellman transforms in terms of the fundamental function of the space. Under some additional assumptions about the space, these conditions are proved to be necessary.

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Authors and Affiliations

  1. Moscow Technology University of Communications and Informatics, USSR

    O. Ya. Berchiyan

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  1. O. Ya. Berchiyan
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Translated from Matematicheskie Zametki, Vol. 53, No. 4, pp. 3–12, April, 1993.

In conclusion, we use the opportunity to express our deep gratitude to B.I.Golubov for his constant attention to this work and also to E.M.Semënov for valuable remarks on the original version of this article.

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Berchiyan, O.Y. On Hardy and Bellman transforms of the Fourier coefficients of functions in symmetric spaces. Math Notes 53, 361–366 (1993). https://doi.org/10.1007/BF01210216

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  • DOI: https://doi.org/10.1007/BF01210216

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