The atomic Hardy space for a general Bessel operator

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.

25 pages, 2 figures