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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2024 Number 11, Pages 97–104 (Mi ivm10038)

This article is cited in 1 paper

Brief communications

Generalizations of Sobolev classes to the metric and topological cases

N. N. Romanovskii

Sobolev Institute of Mathematics of Siberian Branch of the Russian Academy of Sciences, 4 ak. Koptuga str., Novosibirsk, 630090 Russia

Abstract: The paper proposes an approach that makes it possible to describe in the same way classical Sobolev spaces, various generalizations of classical Sobolev spaces for functions defined on a metric or topological space and for functions with values in a metric or topological space, as well as spaces of functions that satisfy certain differential relations.

Keywords: Sobolev class, metric space, topological space.

UDC: 517.518: 517.518

Received: 03.09.2024
Revised: 03.09.2024
Accepted: 26.09.2024

DOI: 10.26907/0021-3446-2024-11-97-104


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:11, 84–90


© Steklov Math. Inst. of RAS, 2026