Hardy spaces for Bessel-Schrödinger operators

2016/03/23 by Kania, Edyta, Preisner, Marcin
#35J10 (Primary) #42B25 #42B30 #43A85 (Secondary) #47D03 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1603.07685

Abstract

Consider the Bessel operator with a potential on L²((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∈ L¹_loc((0,infty), x^a dx) is a non-negative function. By definition, a function f∈ L¹((0,infty), x^a dx) belongs to the Hardy space H¹(L) if sup_t>0 |e^-tL f| ∈ L¹((0,infty), x^a 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 ∈ (0,1) with no additional assumptions on the potential V.

Related

• Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators
• The atomic Hardy space for a general Bessel operator
• Hardy spaces for Fourier--Bessel expansions
• Atomic decompositions for Hardy spaces related to Schr "odinger\n operators
• Hardy spaces related to Schrödinger operators with potentials which are sums of L^p-functions