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Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications

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Abstract

We prove new interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. In particular, these theorems apply to Urysohn integral operators. We also obtain analogs of the Marcinkiewicz–Calderón and Stein–Weiss–Peetre interpolation theorems and establish a criterion of \((p,q)\) quasiweak boundedness of the Urysohn operator.

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Funding

The research of E. D. Nursultanov (Sections 1–4) was supported by the Ministry of Education and Science of the Republic of Kazakhstan, project nos. AP08856479 and AP08956157. The research of V. I. Burenkov presented in Sections 1–4 was supported by the Peoples’ Friendship University of Russia and performed in the S. M. Nikol’skii Mathematical Institute within the Russian Academic Excellence Project. The research of V. I. Burenkov presented in Sections 5–7 was supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.

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Authors and Affiliations

  1. S. M. Nikol’skii Mathematical Institute, RUDN University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    V. I. Burenkov

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

    V. I. Burenkov

  3. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan Str. 11, Nur-Sultan, 010010, Kazakhstan

    E. D. Nursultanov

  4. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, Pushkina Str. 125, Almaty, 050010, Kazakhstan

    E. D. Nursultanov

Authors
  1. V. I. Burenkov
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  2. E. D. Nursultanov
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Correspondence to V. I. Burenkov.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 131–157 https://doi.org/10.4213/tm4129.

Translated by I. Nikitin

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Burenkov, V.I., Nursultanov, E.D. Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications. Proc. Steklov Inst. Math. 312, 124–149 (2021). https://doi.org/10.1134/S0081543821010077

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  • DOI: https://doi.org/10.1134/S0081543821010077

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