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 (-tmathbb {B}_nu ). Then we prove that, in general, H^1 admits an atomic decomposition of local type.