Real, complex and functional analysis

Classes of Sobolev type on quasimetric spaces

A. S. Romanov<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia

Abstract: On quasimetric measure spaces, classes of functions of Sobolev type are defined. In the model cases, analogues of the classical imbedding theorems are proved.

Keywords: quasimetric, Sobolev space, embedding theorem.

UDC: 517.51

MSC: 30L99, 46E35

Received December 7, 2017, published December 14, 2017

DOI: 10.17377/semi.2017.14.124

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