Variation Operators Associated with the Semigroups Generated by Schrodinger Operators with Inverse Square Potentials

Abstract

By {T t }t>0 we denote the semigroup of operators generated by the Friedrichs extension of the Schrödinger operator with the inverse square potential La = −∆+ a |x|2 defined in C∞ c (R n \ {0}). In this paper we establish weighted L-inequalities for the maximal, variation, oscillation and jump operators associated with {t∂ t T a t }t>0, where α ≥ 0 and ∂ α t denotes the Weyl fractional derivative. The range of values p that works is different when a ≥ 0 and when − (n−2) 2 4 < a < 0.