arXiv subjects
Publications and source records attributed to Edyta Kania-Strojec.
We study Hardy space $H^1_L(X)$ related to a self-adjoint operator $L$ defined on Euclidean domain $X \subseteq \mathbb{R}^d$. Under certain assumptions on the heat semigroup $\exp(-tL)$ we prove characterization of $H^1_L(X)$ by the Riesz transforms related to $L$. As an application, we prove the Riesz transform characterization for multidimensional Bessel and Laguerre operators.
We study Hardy spaces associated with a general multidimensional Bessel operator $\mathbb{B}_ν$. 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 $H^1$ for $\mathbb{B}_ν$ in terms of the maximal operator of the semigroup of operators $\exp(-t\mathbb{B}_ν)$. Then we prove that, in general, $H^1$ admits an atomic decomposition of local type.