Abstract
Abstract
In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators
$$ \begin{align*}(\mathcal{H}_{K,\mu}f)(z):=\int_{\mathbb{D}}K(w)f(\sigma_w(z))d\mu(w)\end{align*} $$
on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here,
$\mu $
is a positive Radon measure, K is a
$\mu $
-measurable function on the open unit disk
$\mathbb {D}$
, and
$\sigma _w(z)$
is the classical Möbius transform of
$\mathbb {D}$
.
Publisher
Canadian Mathematical Society