Lp maximal regularity for vector-valued Schrödinger operators

In this paper we consider the vector -valued Schr & ouml;dinger operator -Delta + V , where the potential term V is a matrix -valued function whose entries belong to L 1loc ( R d ) and, for every x E R d , V ( x ) is a symmetric and nonnegative definite matrix, with non positive off -diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in L 1 ( R d , R m ). Assuming further that the minimal eigenvalue of V belongs to some reverse H & ouml;lder class of order q E (1, oo) U {oo}, we obtain maximal inequality in L p ( R d , R m ), for p in between 1 and some q, and generation results. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.