The atomic Hardy space for a general Bessel operator

Abstract We study Hardy spaces associated with a general multidimensional Bessel operator $$\mathbb {B}_\nu $$ B ν . This depends on multiparameter of type $$\nu that is usually restricted to product half-lines. Here we deal the in context, no restrictions parameter. define space $$H^1$$ H 1 for terms maximal semigroup operators $$\exp (-t\mathbb )$$ exp ( - t ) Then prove that, general, admits an atomic decomposition local type.