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

By { T t a } t > 0 we denote the semigroup of operators generated by the Friedrichs extension of the Schrödinger operator with the inverse square potential L a = − Δ + a | x | 2 defined in C c ∞ (ℝ n ∖ { 0 }). In this paper, we establish weighted L p -inequalities for the maximal, variation, oscillation and jump operators associated with { t α ∂ t α T t a } t > 0 , where α ≥ 0 and ∂ t α 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. [ABSTRACT FROM AUTHOR]