2018/04/05 by Runlian Xia, Xiao Xiong, Xia, Runlian +1
Mathematics · #42B30 #46L07 #46L52 #47L65 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1804.01930
openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the operator-valued Triebel-Lizorkin spaces on ℝd. As in the classical case, we connect these spaces with operator-valued local Hardy spaces via Bessel potentials. We show the lifting theorem, and get interpolation results for these spaces. We obtain Littlewood-Paley type, as well as the Lusin type square function characterizations in the general way. Finally, we establish smooth atomic decompositions for the operator-valued Triebel-Lizorkin spaces. These atomic decompositions play a key role in our recent study of mapping properties of pseudo-differential operators with operator-valued symbols.