Operator-valued Triebel–Lizorkin spaces

Xia, R. and Xiong, X. (2018) Operator-valued Triebel–Lizorkin spaces. Integral Equations and Operator Theory, 90, 65. (doi: 10.1007/s00020-018-2491-1)

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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.

Item Type:Articles
Additional Information:The authors are partially supported by the National Natural Science Foundation of China (Grant No. 11301401).
Glasgow Author(s) Enlighten ID:Xia, Dr Runlian
Authors: Xia, R., and Xiong, X.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Integral Equations and Operator Theory
Publisher:Springer Verlag
ISSN (Online):1420-8989
Published Online:24 September 2018

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