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Bilinear Weighted Inequalities with Two-Dimensional Operators

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Abstract—

A characterization of bilinear inequalities with two-dimensional rectangular Hardy operators in weighted Lebesgue spaces is given.

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Funding

The study of the first author (Theorems 1 and 2) was supported by the Russian Science Foundation, project no. 19-11-00087, and was performed at Steklov Mathematical Institute of the Russian Academy of Sciences. The study of the second author (Theorem 3) was supported by the Russian Foundation for Basic Research, project no. 19-01-00223.

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Authors and Affiliations

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

    V. D. Stepanov

  2. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    G. E. Shambilova

Authors
  1. V. D. Stepanov
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  2. G. E. Shambilova
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Corresponding authors

Correspondence to V. D. Stepanov or G. E. Shambilova.

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Translated by N. Berestova

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Stepanov, V.D., Shambilova, G.E. Bilinear Weighted Inequalities with Two-Dimensional Operators. Dokl. Math. 102, 406–408 (2020). https://doi.org/10.1134/S1064562420050415

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  • DOI: https://doi.org/10.1134/S1064562420050415

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