Czechoslovak Mathematical Journal, Vol. 68, No. 4, pp. 953-986, 2018


Generalized Morrey spaces associated to Schrödinger operators and applications

Nguyen Ngoc Trong, Le Xuan Truong

Received January 30, 2017.   Published online July 23, 2018.

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


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Affiliations:   Nguyen Ngoc Trong, University of Science, Vietnam National University Ho Chi Minh City, Deparment of Mathematics, University of Pedagogy Ho Chi Minh City, Vietnam, e-mail: trongnn37@gmail.com; Le Xuan Truong (corresponding author), Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam, e-mail: lexuantruong@tdt.edu.vn


 
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