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arXiv · 1710.00476

Sharp estimates for pseudo-differential operators of type (1,1) on Triebel-Lizorkin and Besov spaces

Bae Jun Park
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Abstract

Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0 d/\min{(1,p)}-d$ for $0<p\leq\infty$. In this work we extend the $F$-boundedness result to $p=\infty$. Additionally, we prove that the operators map $F_{\infty}^{m,1}$ into $bmo$ when $s=0$, and consider H\"ormander's twisted diagonal condition for arbitrary $s\in\mathbb{R}$. We also prove that the restrictions on $s$ are necessary conditions for the boundedness to hold.

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Bae Jun Park. 2017-10-02. Sharp estimates for pseudo-differential operators of type (1,1) on Triebel-Lizorkin and Besov spaces. https://arxiv.org/abs/1710.00476

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