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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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https://hal.archives-ouvertes.fr/hal-01819040
Contributor : Petru Mironescu Connect in order to contact the contributor
Submitted on : Monday, November 19, 2018 - 11:48:36 PM
Last modification on : Monday, June 28, 2021 - 2:26:07 PM
Long-term archiving on: : Wednesday, February 20, 2019 - 4:20:54 PM

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  • HAL Id : hal-01819040, version 3

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

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