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arXiv · 2106.00748

Riesz transform characterizations for multidimensional Hardy spaces

Edyta Kania-Strojec·Marcin Preisner
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Abstract

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.

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Edyta Kania-Strojec, Marcin Preisner. 2021-06-01. Riesz transform characterizations for multidimensional Hardy spaces. https://doi.org/10.1007/s12220-022-00896-1

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