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

2021/05/07 by Almeida, Víctor, Betancor, Jorge J., Rodríguez-Mesa, Lourdes · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.03209

Abstract

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 the space of smooth functions with compact support in ℝⁿ∖\0\. In this paper we establish weighted L^p-inequalities for the maximal, variation, oscillation and jump operators associated with \t^α∂_t^αT_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)

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