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In this paper, we provide the boundedness property of the Riesz transformsassociated to the Schr\"odinger operator $\mathcal{L}=-\Delta + \mathbf{V}$ ina new weighted Morrey space which is the generalized version of many previousMorrey type spaces. The additional potential $\V$ considered in this paper is anon-negative function satisfying the suitable reverse H\"older's inequality.Our results are new and general in many cases of problems. As an application ofthe boundedness property of these singular integral operators, we obtain someregularity results of solutions to Schr\"odinger equations in the new Morreyspace.

On boundedness property of singular integral operators associated to a Schr\"odinger operator in a generalized Morrey space and applications