This article is cited in 4 papers

On embeddings for classes of functions with generalized smoothness on metric spaces

A. S. Romanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Given a metric space with a Borel measure, we consider the classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function summable with some power. We prove embedding theorems for these spaces defined by two different measures satisfying the doubling condition.

Keywords: metric space, measure, Sobolev class, embedding theorem.

UDC: 517.51

Received: 30.10.2003

 English version: Siberian Mathematical Journal, 2004, 45:4, 722–729

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