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On the Boundedness of the Hilbert Transform from Weighted Sobolev Space to Weighted Lebesgue Space

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Abstract

Under some restrictions on weight functions we obtain sufficient conditions for the boundedness of the Hilbert transform from weighted Sobolev space of the first order on the semi-axis to weighted Lebesgue space.

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Acknowledgements

The work of the author presented in Theorems 3.2 and 4.1 was supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. The work presented in the other part of the paper was carried out within the framework of the state task of the Ministry of Science and Higher Education of the Russian Federation to the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences.

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Authors and Affiliations

  1. Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen str. 65, Khabarovsk, Russia, 680000

    Vladimir D. Stepanov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, Russia, 119991

    Vladimir D. Stepanov

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  1. Vladimir D. Stepanov
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Correspondence to Vladimir D. Stepanov.

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Communicated by Kravchenko.

Dedicated to the 80th anniversary of Professor Stefan Samko.

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Stepanov, V.D. On the Boundedness of the Hilbert Transform from Weighted Sobolev Space to Weighted Lebesgue Space. J Fourier Anal Appl 28, 46 (2022). https://doi.org/10.1007/s00041-022-09922-w

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  • DOI: https://doi.org/10.1007/s00041-022-09922-w

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