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Abstract and Applied Analysis
Volume 2013, Article ID 193420, 22 pages
http://dx.doi.org/10.1155/2013/193420
Research Article

Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials

1Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2School of Mathematics and Statics, Wuhan University, Wuhan 430072, China
3School of Sciences, Nantong University, Nantong 226007, China

Received 31 July 2013; Revised 17 September 2013; Accepted 18 September 2013

Academic Editor: Natig M. Atakishiyev

Copyright © 2013 Pengtao Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We employ Meyer wavelets to characterize multiplier space without using capacity. Further, we introduce logarithmic Morrey spaces to establish the inclusion relation between Morrey spaces and multiplier spaces. By fractal skills, we construct a counterexample to show that the scope of the index of is sharp. As an application, we consider a Schrödinger type operator with potentials in .