@inbook {7463,
	title = {Boundedness of pseudodifferential operators on Banach function spaces},
	booktitle = {Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, 242},
	year = {2014},
	pages = {185-195},
	publisher = {Birkh{\"a}user/Springer},
	organization = {Birkh{\"a}user/Springer},
	address = {Basel},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space \(X(\mathbb{R}^n)\) and on its associate space \(X{\textquoteright}(\mathbb{R}^n)\), then a pseudodifferential operator \(\operatorname{Op}(a)\) is bounded on \(X(\mathbb{R}^n)\) whenever the symbol \(a\) belongs to the H{\"o}rmander class \(S_{\rho,\delta}^{n(\rho-1)}\) with \(0\&lt;\rho\le 1\), \(0\le\delta\&lt;1\) or to the the Miyachi class \(S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)\) with \(0\le\delta\le\rho\le 1\), \(0\le\delta\&lt;1\),  and \(\varkappa\&gt;0\). This result is applied to the case of variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R}^n)\).</p>
},
	url = {http://link.springer.com/chapter/10.1007\%2F978-3-0348-0816-3_10},
	author = {Karlovich, Alexei Yu.},
	editor = {Bastos, Maria Am{\'e}lia and Lebre, Amarino and Samko, Stefan and Spitkovsky, Ilya M.}
}
