This article is cited in 4 papers

Marcinkiewicz's interpolation theorem for linear operators on net spaces

A. K. Kalidolday^a, E. D. Nursultanov<sup>abc

a</sup> Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 5 Munaitpasov St, 010008 Astana, Kazakhstan
^b Department of Mathematics and Informatics, M.V. Lomonosov Moscow State University (Kazakhstan branch), 11 Kazhimukan St, 010010 Astana, Kazakhstan
^c Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan

Abstract: In this paper, we study the interpolation properties of the net spaces $N_{p,q}(M)$. We prove some analogue of Marcinkiewicz's interpolation theorem. This theorem allows to obtain the strong boundedness of linear operators in the net spaces from the weak boundedness of these operators in the net spaces with local nets.

Keywords and phrases: interpolation spaces, net spaces, linear operators.

MSC: 46B70

Received: 25.07.2021

Language: English

DOI: 10.32523/2077-9879-2022-13-4-61-69

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