arXiv 1804.034352018-04-10math.OAmath.CAmath.FA

Mapping properties of operator-valued pseudo-differential operators

Runlian Xia, Xiao Xiong

备注：: 37 pages

英文摘要：

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 $F_1^{α,c}(\mathbb{R}^d,\mathcal{M})$ obtained in our previous paper, we establish the $F_1^{α,c}$-regularity of regular symbols for every $α\in \mathbb{R}$, and the $F_1^{α,c}$-regularity of forbidden symbols for $α>0$. As applications, we obtain the same results on the usual and quantum tori.

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