Hardy spaces for Bessel-Schr\"odinger operators
Classical Analysis and ODEs
2017-09-15 v2 Analysis of PDEs
Functional Analysis
Abstract
Consider the Bessel operator with a potential on L^2((0,infty), x^a dx), namely Lf(x) = -f"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\in L^1_{loc}((0,infty), x^a dx) is a non-negative function. By definition, a function f\in L^1((0,infty), x^a dx) belongs to the Hardy space H^1(L) if sup_{t>0} |e^{-tL} f| \in L^1((0,infty), x^a dx). Under certain assumptions on V we characterize the space H^1(L) in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to L for a \in (0,1) with no additional assumptions on the potential V.
Cite
@article{arxiv.1603.07685,
title = {Hardy spaces for Bessel-Schr\"odinger operators},
author = {Edyta Kania and Marcin Preisner},
journal= {arXiv preprint arXiv:1603.07685},
year = {2017}
}