Singular Integral and Local Hardy Spaces in Dunkl Setting

The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in $L^2$ space and the theory of nonhomogeneous singular integral operators as pivotal components.