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Hardy-Goldberg operator and its conjugate one in hardy spaces and BMO \((\mathbb{T})\)

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Abstract

The Hardy operator is well-known in harmonic analysis. It transforms the sequence of Fourier coefficients of a function to a the sequence of its arithmetic means. In the paper we consider the Hardy-Goldberg operator generalizing the Hardy operator and its conjugate one. We prove the boundedness of the Hardy-Goldberg operator in the real Hardy space and of its analog in the Hardy space on the disc. We establish the boundedness of the conjugate Hardy-Goldberg operator in the periodic BMO andVMO spaces.

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Authors and Affiliations

  1. Saratov State University, ul. Astrakhanskya 83, Saratov, 410012, Russia

    S. S. Volosivets

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  1. S. S. Volosivets
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Correspondence to S. S. Volosivets.

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Original Russian Text © S.S. Volosivets, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 2, pp. 30–34.

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Volosivets, S.S. Hardy-Goldberg operator and its conjugate one in hardy spaces and BMO \((\mathbb{T})\) . Russ Math. 59, 14–24 (2015). https://doi.org/10.3103/S1066369X15020036

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  • DOI: https://doi.org/10.3103/S1066369X15020036

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