info:eu-repo/semantics/article
Weighted Inequalities for Schrödinger Type Singular Integrals
Fecha
2019-06-10Registro en:
Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo; Weighted Inequalities for Schrödinger Type Singular Integrals; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 25; 3; 10-6-2019; 595–632
1069-5869
1531-5851
CONICET Digital
CONICET
Autor
Bongioanni, Bruno
Harboure, Eleonor Ofelia
Quijano, Pablo
Resumen
Related to the Schrödinger operator L= - Δ + V, the behaviour on Lp 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 ρ: X→ R+ 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 ρ. We analyse their behaviour on weighted Lp 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.