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

By {T-t(a)}t>0 we denote the semigroup of operators generated by the Friedrichs extension of the Schrodinger operator with the inverse square potential L-a = -Delta + a/vertical bar x vertical bar(2) defined in C-c(infinity) (R-n\{0}). In this paper, we establish weighted L-p-inequalities for the maximal, variation, oscillation and jump operators associated with {t(alpha)partial derivative T-alpha(t)t(alpha)}t> o, where alpha >= 0 and partial derivative(alpha)(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.

Automated summary

This paper investigates the semigroup of operators generated by the Friedrichs extension of the Schrodinger operator with the inverse square potential. Weighted L-p inequalities are established for operators associated with the Weyl fractional derivative. The range of suitable p values differs depending on the value of a.