2010/01/10 by Wen Yuan, Yoshihiro Sawano, Yuan, Wen +3
Mathematics · #42C40 (Secondary) #46E35 (Primary) #47G30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA #msc:42C40 #msc:46E35 #msc:47G30
paper · pdf · doi:10.48550/arxiv.1001.1510
30 pages, J. Math. Anal. Appl. (to appear).
openalex publication_date 2010/01/10 · arxiv created 2010/04/11 · arxiv updated 2010/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p∈(1,∞), q∈[1,∞), s∈ℝ and τ∈[0, 1-\frac1max\p,q\]. In this paper, the authors establish the φ-transform characterizations of Besov-Hausdorff spaces B Hp,qs,τ(ℝn) and Triebel-Lizorkin-Hausdorff spaces F Hp,qs,τ(ℝn) (q>1); as applications, the authors then establish their embedding properties (which on B Hp,qs,τ(ℝn) is also sharp), smooth atomic and molecular decomposition characterizations for suitable τ. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in B Hp,qs,τ(ℝn) and F Hp,qs,τ(ℝn) (q>1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p∈(1,∞) and q∈[1,∞) by taking τ=0.