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Hardy–Steklov Operators and Duality Principle in Weighted Sobolev Spaces of the First Order

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Abstract

Boundedness criteria for the Hardy–Steklov operator in Lebesgue spaces on the real axis are presented. As applications, two-sided estimates for the norms of spaces associated with weighted Sobolev spaces of the first order with various weight functions and summation parameters are established.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    V. D. Stepanov

  2. Computing Center, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, 680000, Russia

    E. P. Ushakova

Authors
  1. V. D. Stepanov
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  2. E. P. Ushakova
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Corresponding author

Correspondence to V. D. Stepanov.

Additional information

Original Russian Text © V.D. Stepanov, E.P. Ushakova, 2018, published in Doklady Akademii Nauk, 2018, Vol. 480, No. 2, pp. 150–154.

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Stepanov, V.D., Ushakova, E.P. Hardy–Steklov Operators and Duality Principle in Weighted Sobolev Spaces of the First Order. Dokl. Math. 97, 232–235 (2018). https://doi.org/10.1134/S1064562418030092

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