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

Burenkov V.I. Nursultanov E.D.
March 2021 Pleiades journals

Proceedings of the Steklov Institute of Mathematics
2021 #312 Issue 1 124 - 149 pp.

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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S. M. Nikol’skii Mathematical Institute, RUDN University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russian Federation
Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan Str. 11, Nur-Sultan, 010010, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, Pushkina Str. 125, Almaty, 050010, Kazakhstan

S. M. Nikol’skii Mathematical Institute
Steklov Mathematical Institute of Russian Academy of Sciences
Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modeling

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