Asymptotic Behaviour of fractional seminorms

2024/08/29 by Ahmed Dughayshim, Dughayshim, Ahmed
Computer Science · Mathematics · #42B35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2408.16894

openalex publication_date 2024/08/29 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28

Abstract

We obtain asymptotically sharp identification of fractional Sobolev spaces W^s_p,q, extension spaces E^s_p,q, and Triebel-Lizorkin spaces F^s_p,q. In particular we obtain for W^s_p,q and E^s_p,q a stability theory a la Bourgain-Brezis-Mironescu as s → 1, answering a question raised by Brazke--Schikorra--Yung. Part of the results are new even for p=q.

Citations

• Limits at infinity for functions in fractional Sobolev spaces
• Inequalities In Homogeneous Triebel-Lizorkin And Besov-Lipschitz Spaces
• On Function Spaces with Mixed Norms --- A Survey
• A characterisation of the Besov-Lipschitz and Triebel-Lizorkin spaces using Poisson like kernels
• Some Maximal Inequalities

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