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Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis

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Abstract

Estimates of the norms of spaces associated to weighted first-order Sobolev spaces with various weight functions and summation parameters are established. As the main technical tool, boundedness criteria for the Hardy–Steklov integral operator with variable limits of integration in Lebesgue spaces on the real axis are used.

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Authors and Affiliations

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

    V. D. Stepanov & E. P. Ushakova

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

    V. D. Stepanov & E. P. Ushakova

Authors
  1. V. D. Stepanov
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  2. E. P. Ushakova
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Correspondence to V. D. Stepanov or E. P. Ushakova.

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Russian Text © V. D. Stepanov, E. P. Ushakova, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 1, pp. 108–122.

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Stepanov, V.D., Ushakova, E.P. Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis. Math Notes 105, 91–103 (2019). https://doi.org/10.1134/S0001434619010103

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  • DOI: https://doi.org/10.1134/S0001434619010103

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