What question did this study set out to answer?

The aim is to construct a new scale of Sobolev-type spaces and demonstrate their embedding properties.

April 3, 2026

Generalizations of Sobolev Spaces and Embedding Theorems

Key Points

The aim is to construct a new scale of Sobolev-type spaces and demonstrate their embedding properties.
Constructed a scale of Sobolev-type spaces that includes classical and Slobodetskii types.
Defined Sobolev spaces for functions on a general topological space.
Proved embedding theorems for these new Sobolev spaces.
Established a framework for defining Sobolev spaces with differential relations.
Proved new embedding theorems depending on the topological characteristics of the space.

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.

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Generalizations of Sobolev Spaces and Embedding Theorems

Key Points

Abstract

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