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Generalized Morrey spaces associated to Schrödinger operators and applications

Nguyen Ngoc TrongLe Xuan Truong — 2018

Czechoslovak Mathematical Journal

We first introduce new weighted Morrey spaces related to certain non-negative potentials satisfying the reverse Hölder inequality. Then we establish the weighted strong-type and weak-type estimates for the Riesz transforms and fractional integrals associated to Schrödinger operators. As an application, we prove the Calderón-Zygmund estimates for solutions to Schrödinger equation on these new spaces. Our results cover a number of known results.

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