Wavelets, Multiplier spaces and application to Schrödinger type operators with non-smooth potentials

In this paper, we employ Meyer wavelets to characterize multiplier spaces between Sobolev spaces without using capacity. Further, we introduce logarithmic Morrey spaces $M^{t,τ}_{r,p}(\mathbb{R}^{n})$ to establish the inclusion relation between Morrey spaces and multiplier spaces. By wavelet characterization and fractal skills, we construct a counterexample to show that the scope of the index $τ$ of $M^{t,τ}_{r,p}(\mathbb{R}^{n})$ is sharp. As an application, we consider a Schrödinger type operator with potentials in $M^{t,τ}_{r,p}(\mathbb{R}^{n})$.

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