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Abstract <p>A scale of Sobolev-type spaces is constructed including classical Sobolev and Sobolev–Slobodetskii spaces, spaces consisting of Sobolev functions satisfying certain differential relations. This approach allows defining Sobolev spaces for functions defined on a topological space and to prove embedding theorems.</p>

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Generalizations of Sobolev Spaces and Embedding Theorems

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • N. N. Romanovskii

摘要

Abstract

A scale of Sobolev-type spaces is constructed including classical Sobolev and Sobolev–Slobodetskii spaces, spaces consisting of Sobolev functions satisfying certain differential relations. This approach allows defining Sobolev spaces for functions defined on a topological space and to prove embedding theorems.