Operator-Valued Triebel–Lizorkin Spaces
| Autor: | Runlian Xia, Xiao Xiong |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Algebra and Number Theory 010102 general mathematics Mathematics::Classical Analysis and ODEs Hardy space 01 natural sciences Square (algebra) Multiplier (Fourier analysis) symbols.namesake Operator (computer programming) Fourier transform 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Analysis Bessel function Mathematics |
| Zdroj: | Integral Equations and Operator Theory. 90 |
| ISSN: | 1420-8989 0378-620X |
| Popis: | 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 $$\mathbb {R}^d$$ . 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. |
| Databáze: | OpenAIRE |
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