Variation operators for semigroups and Riesz transforms acting on weighted Lp and BMO spaces in the Schrödinger setting

Abstract

In this paper, we extend the results of Schrödinger type operators (Betancor et al., Rev Mat Complut 26:485–534, 2013) and (Betancor et al., Potential Anal 38:711–739, 2013) to the weighted Lp(Rn) and BMO spaces respectively, with the new type weight class defined (Bongioanni et al., J Math Anal Appl 373:563–579, 2011) which includes the Muckenhoupt class.