Fractional Sobolev embeddings and algebra property: A dyadic view

2024/12/16 by Ruiz, Patricia Alonso, Fragkiadaki, Valentia · 2 citations
#26A33 #42A99 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2412.12051

Abstract

This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space H^s(ℝ) by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approach without Fourier transform that may be transferred to settings where the latter is not available. Explicit counterexamples are constructed to show the failure of the algebra property in the low-regularity regime.

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• Dyadic fractional Sobolev spaces: Embeddings and algebra property
• A measure theoretic approach to Lipschitz regularity and its Haar type wavelet analysis

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