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

Abstract

We employ Meyer wavelets to characterize multiplier space Xr,pt(ℝn) without using capacity. Further, we introduce logarithmic Morrey spaces Mr,pt,τ(ℝn) 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 τ of Mr,pt,τ(ℝn) is sharp. As an application, we consider a Schrödinger type operator with potentials in Mr,pt,τ(ℝn).