Weighted Inequalities for Schrödinger Type Singular Integrals

BONGIOANNI, B.; QUIJANO, P.; HARBOURE, E.

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

BIRKHAUSER BOSTON INC

Año: 2018 p. 1 - 38

1069-5869

Related to the Schrödinger operator (Formula presented.), the behaviour on (Formula presented.) of several first and second order Riesz transforms was studied by Shen (Ann Inst Fourier (Grenoble) 45(2):513?546, 1995). Under his assumptions on V, a critical radius function (Formula presented.) can be associated, with the property that its variation is controlled by powers. Given such a function, we introduce a class of singular integral operators whose kernels have some extra decay related to (Formula presented.). We analyse their behaviour on weighted (Formula presented.) and BMO-type spaces. Here, the weights as well as the regularity spaces depend only on the critical radius function. When our results are set back into the Schrödinger context, we obtain weighted inequalities for all the Riesz transforms initially appearing in Shen (1995). Concerning the action of Schrödinger singular integrals on regularity spaces, we extend some previous work of Ma et al.