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- W4384933360 abstract "Abstract In this note, we consider a pseudo-differential operator $T_a$ defined as begin{align*} T_a f(x)=int_{mathbb{R}^n}e^{2pi ixcdotxi}a(x,xi)widehat{f}(xi)dxi. end{align*} It is well-known that $T_a$ is not bounded on $L^2$ in general when $a$ belongs to the forbidden H{o}rmander class $S^{n(rho-1)/2}_{rho,1},0leq rho leq 1$. In this note, when $s>0,0leq rho leq 1,1leq rleq 2$ and $ain S^{n(rho-1)/r}_{rho,1}$, we prove that $T_a$ is bounded on the Triebel-Lizorkin space $F^s_{p,q}$ if $r 0$, if $2 Mathematics Subject Classification: 42B20 · 35S30." @default.
- W4384933360 created "2023-07-22" @default.
- W4384933360 creator A5013290006 @default.
- W4384933360 creator A5036614817 @default.
- W4384933360 date "2023-07-20" @default.
- W4384933360 modified "2023-10-05" @default.
- W4384933360 title "Pseudo-differential operators with forbidden symbols on Triebel-Lizorkin spaces" @default.
- W4384933360 doi "https://doi.org/10.21203/rs.3.rs-3170718/v1" @default.
- W4384933360 hasPublicationYear "2023" @default.
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