# Boundedness of pseudodifferential operators on Banach function spaces

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## Abstract

We show that if the Hardy-Littlewood maximal operator is bounded on aseparable Banach function space $X(\R^n)$ and on its associate space$X'(\R^n)$, then a pseudodifferential operator $\Op(a)$ is boundedon $X(\R^n)$ whenever the symbol $a$ belongs to the H\"ormander class$S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$with $0\le\delta\le\rho\le 1$, $0\le\delta<1$, and $\varkappa>0$.This result is applied to the case of variable Lebesgue spaces$L^{p(\cdot)}(\mathbb{R}^n)$.
Original language Unknown Operator Theory: Advances and Applications 185-195 978-3-0348-0816-3 https://doi.org/10.1007/978-3-0348-0816-3_10 Published - 1 Jan 2014 Operator Theory, Operator Algebras and Applications. Workshop on Operator Theory, Operator Algebras and Applications, Lisboa, 2012 - Duration: 1 Jan 2012 → …

### Conference

Conference Operator Theory, Operator Algebras and Applications. Workshop on Operator Theory, Operator Algebras and Applications, Lisboa, 2012 1/01/12 → …