2023/09/04 by Jae-Hwan Choi, Choi, Jae-Hwan, Jin Bong Lee +5
Mathematics · Medicine · #42B25 #42B35 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Soft tissue tumor case studies
paper · pdf · doi:10.48550/arxiv.2309.01359
openalex publication_date 2023/09/04 · openalex created_date 2023/09/08 · openalex updated_date 2026/07/28
In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are other norms arising in the theory of partial differential equations such as Sobolev-Slobodeckij spaces. It is known that two norms are equivalent when one considers constant regularity function spaces without weights. We show that the equivalence still holds for variable smoothness and weights, which is accomplished by making use of shifted maximal functions, Peetre's maximal functions, and the reverse Hölder inequality. Moreover, we obtain a weighted regularity estimate for time-fractional evolution equations and a generalized Sobolev embedding theorem without weights.