This article is cited in 2 papers

Composition operators between Sobolev spaces on metric measure spaces. I

D. A. Sboev

Novosibirsk State University, Novosibirsk, Russia

Abstract: We obtain a description of homeomorphisms inducing bounded composition operators between Sobolev spaces whose functions are defined on metric measure spaces. As a consequence, we establish a characterization of quasiconformal mappings in metric measure spaces.

Keywords: composition operator, metric measure space, Sobolev space, ${\mathcal Q}_{p}$-homeomorphism, mapping of finite distortion, quasiconformal mapping.

UDC: 517.54

MSC: 35R30

Received: 24.06.2025
Revised: 24.06.2025
Accepted: 03.07.2025

DOI: 10.33048/smzh.2025.66.515

 English version: Siberian Mathematical Journal, 2025, 66:5, 1254–1269