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arXiv · 2004.14434

The atomic Hardy space for a general Bessel operator

Edyta Kania-Strojec
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Abstract

We study Hardy spaces associated with a general multidimensional Bessel operator $\mathbb{B}_\nu$. This operator depends on a multiparameter of type $\nu$ 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 $H^1$ for $\mathbb{B}_\nu$ in terms of the maximal operator of the semigroup of operators $\exp(-t\mathbb{B}_\nu)$. Then we prove that, in general, $H^1$ admits an atomic decomposition of local type.

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Edyta Kania-Strojec. 2020-04-29. The atomic Hardy space for a general Bessel operator. https://arxiv.org/abs/2004.14434

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