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arXiv · 1702.02033

Domains of type 1,1 operators: a case for Triebel--Lizorkin spaces

Jon Johnsen
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Abstract

Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$ for $1\le p<\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin spaces. H\"ormander's condition on the twisted diagonal is extended to this framework, using a general support rule for Fourier transformed pseudo-differential operators.

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Jon Johnsen. 2017-02-07. Domains of type 1,1 operators: a case for Triebel--Lizorkin spaces. https://doi.org/10.1016/j.crma.2004.05.008

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