## Abstract and Applied Analysis

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

#### Abstract

We employ Meyer wavelets to characterize multiplier space ${X}_{r,p}^{t}\left({ℝ}^{n}\right)$ without using capacity. Further, we introduce logarithmic Morrey spaces ${M}_{r,p}^{t,\tau }\left({ℝ}^{n}\right)$ 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 $\tau$ of ${M}_{r,p}^{t,\tau }\left({ℝ}^{n}\right)$ is sharp. As an application, we consider a Schrödinger type operator with potentials in ${M}_{r,p}^{t,\tau }\left({ℝ}^{n}\right)$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 193420, 22 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512161

Digital Object Identifier
doi:10.1155/2013/193420

Mathematical Reviews number (MathSciNet)
MR3132555

Zentralblatt MATH identifier
1298.42039

#### Citation

Li, Pengtao; Yang, Qixiang; Zhu, Yueping. Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials. Abstr. Appl. Anal. 2013 (2013), Article ID 193420, 22 pages. doi:10.1155/2013/193420. https://projecteuclid.org/euclid.aaa/1393512161

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