<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karlovich, Alexei Yu.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Bastos, Maria Amélia</style></author><author><style face="normal" font="default" size="100%">Lebre, Amarino</style></author><author><style face="normal" font="default" size="100%">Samko, Stefan</style></author><author><style face="normal" font="default" size="100%">Spitkovsky, Ilya M.</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Boundedness of pseudodifferential operators on Banach function spaces</style></title><secondary-title><style face="normal" font="default" size="100%">Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, 242</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/chapter/10.1007%2F978-3-0348-0816-3_10</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Birkhäuser/Springer</style></publisher><pub-location><style face="normal" font="default" size="100%">Basel</style></pub-location><pages><style face="normal" font="default" size="100%">185-195</style></pages><abstract><style face="normal" font="default" size="100%">&lt;script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'&gt;&lt;/script&gt;&lt;p&gt;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 \(X'(\mathbb{R}^n)\), then a pseudodifferential operator \(\operatorname{Op}(a)\) is bounded on \(X(\mathbb{R}^n)\) whenever the symbol \(a\) belongs to the Hörmander class \(S_{\rho,\delta}^{n(\rho-1)}\) with \(0&amp;lt;\rho\le 1\), \(0\le\delta&amp;lt;1\) or to the the Miyachi class \(S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)\) with \(0\le\delta\le\rho\le 1\), \(0\le\delta&amp;lt;1\),  and \(\varkappa&amp;gt;0\). This result is applied to the case of variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R}^n)\).&lt;/p&gt;
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