Convolution operators on the weighted Herz-type Hardy spaces
Let \(0<p\leq 1 <q<\infty\) and \(w \in A_1\) (the weight class of Muckenhoupt). In this paper, the author first establishes a weighted molecular characterization for the weighted Herz-type Hardy spaces \(H\dot{K}_q^{n(1/p-1/q),p}(w,w)\) and \(HK_q^{n(1/p-1/q),p}(w,w)\). Using this characterization, the author then obtains the boundedness of the convolution operator \(Tf=k*f\) in the weighted Herz-type Hardy spaces when \(p\leq 1\). In particular, the boundedness of the Hilbert transform and the Riesz transforms in these weighted Herz-type Hardy spaces when \(0<p\leq 1\) can be deduced from these results.
scientific article; zbMATH DE number 5013602
scientific article