Generalized Morrey spaces associated to Schrödinger operators and applications

Trong, Nguyen Ngoc ; Truong, Le Xuan

Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 953-986

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2018.0039-17

Classification : 42B20, 42B35
Keywords: Morrey space; Schrödinger operator; Riesz transform; fractional integral; Calderón-Zygmund estimate

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