Geodesic
Generalized Morrey spaces associated to Schrödinger operators and applications
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 953-986.

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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.
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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     title = {Generalized {Morrey} spaces associated to {Schr\"odinger} operators and applications},
     journal = {Czechoslovak Mathematical Journal},
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Trong, Nguyen Ngoc; Truong, Le Xuan. Generalized Morrey spaces associated to Schrödinger operators and applications. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 953-986. doi : 10.21136/CMJ.2018.0039-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0039-17/

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