Mapping properties of operator-valued pseudo-differential operators

2018/04/10 by Runlian Xia, Xiao Xiong, Xia, Runlian +1
Mathematics · #Advanced Operator Algebra Research #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1804.03435

Abstract

In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces F₁^α,c(ℝ^d,M) obtained in our previous paper, we establish the F₁^α,c-regularity of regular symbols for every α∈ ℝ, and the F₁^α,c-regularity of forbidden symbols for α>0. As applications, we obtain the same results on the usual and quantum tori.

Citations

• Some new function spaces and their applications to Harmonic analysis

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