The atomic Hardy space for a general Bessel operator

2020/04/29 by Kania-Strojec, Edyta
#42B25 #42B30 (primary) #47D03 (secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.14434

Abstract

We study Hardy spaces associated with a general multidimensional Bessel operator \mathbbB_ν. This operator depends on a multiparameter of type ν that is usually restricted to a product of half-lines. Here we deal with the Bessel operator in the general context, with no restrictions on the type parameter. We define the Hardy space H¹ for \mathbbB_ν in terms of the maximal operator of the semigroup of operators exp(-t\mathbbB_ν). Then we prove that, in general, H¹ admits an atomic decomposition of local type.

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• Hardy spaces for Bessel-Schrödinger operators
• Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators
• Hardy spaces for Fourier--Bessel expansions
• Characterizations of product Hardy spaces in Bessel setting
• Local atomic decompositions for multidimensional Hardy spaces