Dyadic fractional Sobolev spaces: Embeddings and algebra property

2025/11/18 by Ruiz, Patricia Alonso, Fragkiadaki, Valentia
Mathematics · Engineering · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Numerical methods in engineering

paper · doi:10.48550/arxiv.2511.14877

Abstract

This paper studies a dyadic version of fractional Sobolev spaces in ℝⁿ for n≥ 1. It provides new proofs of the corresponding fractional Sobolev embedding as well as the algebra property of the spaces, which rely solely on dyadic techniques and in particular bypass the Fourier transform. Specific counterexamples are constructed to verify the failure of the algebra property in low-regularity ranges.

Citations

• Fractional Sobolev embeddings and algebra property: A dyadic view
• Partial derivatives, singular integrals and Sobolev Spaces in dyadic settings
• The Haar System in Triebel-Lizorkin Spaces: Endpoint Results
• On uniform boundedness of dyadic averaging operators in spaces of\n Hardy-Sobolev type
• Two weight norm inequalities for fractional integral operators and\n commutators

Related

• Fractional Sobolev embeddings and algebra property: A dyadic view
• On New Families of Fractional Sobolev Spaces
• Hitchhiker's guide to the fractional Sobolev spaces
• Fractional Orlicz-Sobolev embeddings into Campanato type spaces
• Characterizations of Fractional Sobolev Spaces From the Perspective of Riemann-Liouville Operators