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Journal Articles Revue roumaine de mathématiques pures et appliquées Year : 2018

The role of the Hardy type inequalities in the theory of function spaces

Abstract

We illustrate the crucial importance of the Hardy type inequalities in the study of function spaces, especially of fractional regularity. Immediate applications include Sobolev and Morrey type embeddings, and properties of the superposition operator $f\mapsto \Phi\circ f$. Another fundamental consequence is the trace theory of weighted Sobolev spaces. In turn, weighted Sobolev spaces are useful in the regularity theory of the superposition operators. More involved applications, that we present in the final section, are related to Sobolev spaces of maps with values into manifolds.
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Dates and versions

hal-01819040 , version 1 (19-06-2018)
hal-01819040 , version 2 (28-06-2018)
hal-01819040 , version 3 (19-11-2018)

Identifiers

  • HAL Id : hal-01819040 , version 3

Cite

Petru Mironescu. The role of the Hardy type inequalities in the theory of function spaces. Revue roumaine de mathématiques pures et appliquées, 2018, 63 (4), pp.447-525. ⟨hal-01819040v3⟩
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