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Hardy spaces for Bessel-Schrödinger operators (1603.07685v2)

Published 23 Mar 2016 in math.CA, math.AP, and math.FA

Abstract: Consider the Bessel operator with a potential on L2((0,infty), xa dx), namely Lf(x) = -f"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\in L1_{loc}((0,infty), xa dx) is a non-negative function. By definition, a function f\in L1((0,infty), xa dx) belongs to the Hardy space H1(L) if sup_{t>0} |e{-tL} f| \in L1((0,infty), xa dx). Under certain assumptions on V we characterize the space H1(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.

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