Variation operators associated with the semigroups generated by Schrödinger operators with inverse square potentials

Abstract

By [Formula: see text] we denote the semigroup of operators generated by the Friedrichs extension of the Schrödinger operator with the inverse square potential [Formula: see text] defined in [Formula: see text]. In this paper, we establish weighted [Formula: see text]-inequalities for the maximal, variation, oscillation and jump operators associated with [Formula: see text], where [Formula: see text] and [Formula: see text] denotes the Weyl fractional derivative. The range of values [Formula: see text] that works is different when [Formula: see text] and when [Formula: see text].