Fractional Sobolev embeddings and algebra property: A dyadic view

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ruiz, Patricia Alonso, Fragkiadaki, Valentia
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913946429030400
author Ruiz, Patricia Alonso
Fragkiadaki, Valentia
author_facet Ruiz, Patricia Alonso
Fragkiadaki, Valentia
contents This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_12051
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Fractional Sobolev embeddings and algebra property: A dyadic view
Ruiz, Patricia Alonso
Fragkiadaki, Valentia
Classical Analysis and ODEs
Functional Analysis
42B35, 26A33, 42A99
This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ 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.
title Fractional Sobolev embeddings and algebra property: A dyadic view
topic Classical Analysis and ODEs
Functional Analysis
42B35, 26A33, 42A99
url https://arxiv.org/abs/2412.12051