This article is cited in 5 papers

Embedding theorems for a certain function class of Sobolev type 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 $\mu$, we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function $p$-summable with respect to $\mu$. We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.

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

UDC: 517.51

Received: 25.06.2003

 English version: Siberian Mathematical Journal, 2004, 45:2, 376–387

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