J. Pseudo-Differ. Oper. Appl. (2016) 7:595–607 DOI 10.1007/s11868-016-0158-8 Weighted Morrey and weighted fractional Sobolev–Morrey spaces estimates for a large class of pseudo-differential operators with smooth symbols F. Gurbuz 1 Received: 29 February 2016 / Accepted: 22 March 2016 / Published online: 2 April 2016 © Springer International Publishing 2016 Abstract In this paper, we study the boundedness results for a large class of pseudo-differential operators with smooth symbols on weighted Morrey and Weighted fractional Sobolev–Morrey spaces, respectively. Keywords Weighted Morrey Space · Weighted fractional Sobolev–Morrey Space · Maximal operator · Pseudo-differential Operator · A p weights Mathematics Subject Classification 42B20 · 42B25 · 46E35 1 Introduction The classical Morrey spaces have been introduced by Morrey in [7] to study the local behavior of solutions of second order elliptic partial differential equations(PDEs). In recent years there has been an explosion of interest in the study of the boundedness of operators on Morrey-type spaces. It has been obtained that many properties of solu- tions to PDEs are concerned with the boundedness of some operators on Morrey-type spaces. In fact, better inclusion between Morrey and Hölder spaces allows to obtain higher regularity of the solutions to different elliptic and parabolic boundary prob- lems. Chiarenza and Frasca [3] have obtained the boundedness of Hardy–Littlewood maximal operator, the fractional integral operator and a singular integral operator in the Morrey spaces. The boundedness of fractional integral operator has been origi- nally studied by Adams [1]. On the other hand, it is very important to study weighted B F. Gurbuz feritgurbuz84@hotmail.com 1 Department of Mathematics, Faculty of Science, Ankara University, Tando˘ gan, 06100 Ankara, Turkey