Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators (2010.13895v3)

Published 26 Oct 2020 in math.AP and math.CA

Abstract: We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C{r}{*}S{m}{1,\delta}$ classes that have limited regularity in the $x$ variable. We show that the associated pseudodifferential operator $a(x,D)$ maps between Sobolev spaces $\mathcal{H}{s,p}_{FIO}(\mathbb{R}{n})$ and $\mathcal{H}{t,p}_{FIO}(\mathbb{R}{n})$ over the Hardy space for Fourier integral operators $\mathcal{H}{p}_{FIO}(\mathbb{R}{n})$. Our main result implies that for $m=0$, $\delta=1/2$ and $r>n-1$, $a(x,D)$ acts boundedly on $\mathcal{H}{p}_{FIO}(\mathbb{R}{n})$ for all $p\in(1,\infty)$.

Summary

We haven't generated a summary for this paper yet.