Interpolation theorems for nonlinear operators in general Morrey-type spaces and their applications
type: Item
instance of: scholarly article
title: Interpolation theorems for nonlinear operators in general Morrey-type spaces and their applications
DOI: 10.1134/S0081543821010077
author: N. E. Zubov
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2021-05-05T00:00:00Z
review text: In the paper under review the authors define a much more general class of Morrey-type spaces. They present a number of properties of the new Morrey-type spaces and describe the classes of nonlinear operators under consideration (partially quasi-additive operators) and give examples of operators from these classes, including Urysohn integral operators. They establish general interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. As applications, they obtain analogs of the Marcinkiewicz-Calderón and Stein-Weiss-Peetre interpolation theorems. At last, they prove a quasiweak boundedness criterion for a wide class of Urysohn integral operators.
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 7343913
zbMATH Keywords: interpolation theorem
zbMATH Keywords: Morrey-type space
zbMATH Keywords: nonlinear operators
zbMATH Keywords: Urysohn integral operators
reviewed by: Fayou Zhao
MaRDI profile type: Publication
cites work: Spaces of stochastic processes, interpolation theorems
cites work: Q3081803
cites work: Q4943985
cites work: Necessary and sufficient conditions for the boundedness of the maximal operator in local Morrey-type spaces
cites work: Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
cites work: Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces
cites work: Necessary and sufficient conditions for the boundedness of the fractional maximal operator in local Morrey-type spaces
cites work: Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries
cites work: Description of interpolation spaces for local Morrey-type spaces
cites work: INTERPOLATION THEOREMS FOR NONLINEAR URYSOHN INTEGRAL OPERATORS IN GENERAL MORREY-TYPE SPACES
cites work: Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations
cites work: Weak*-sequential closure and the characteristic of subspaces of conjugate Banach spaces
cites work: Q5521918
cites work: Q4761682
cites work: Q5522633
cites work: The role of Morrey spaces in the study of Navier-Stokes and Euler equations
cites work: Multipliers and Morrey spaces
cites work: Interpolation methods for stochastic processes spaces
cites work: Net spaces and boundedness of integral operators
cites work: Q3940347
cites work: A necessary and sufficient condition for boundedness and continuity of a certain class of Uryson operators
cites work: On the theory of \({\mathcal L}_{p, \lambda}\) spaces
cites work: A new approach in interpolation spaces
cites work: Corrigenda to ``Unique continuation for Schrödinger operators'' and a remark on interpolation of Morrey spaces
cites work: £(p,λ)‐spaces and interpolation
cites work: Interpolation of Operators with Change of Measures
full work available at URL: s0081543821010077
OpenAlex ID: W3157249775
description: scientific article; zbMATH DE number 7343913