Let $H(\mathbb B)$ denote the space of all holomorphic
functions on the unit ball
$\mathbb B$ of $\mathbb C^n$ and $\Re h(z)=\sum_{j=1}^nz_j\frac{\pt h}{\pt z_j}(z)$ the
radial derivative of $h.$ Motivated by recent results by S. Li and
S. Stević , in this paper
we study the boundedness and compactness of the following integral
operator
$$ L_gf(z)= \int_0^1
\Re f(tz) g(tz)\frac{dt}{t},\quad z\in \mathbb B,
$$
between the Hardy space $H^2$ and weighted Bergman spaces.
@article{1299766488,
author = {Zhu, Xiangling},
title = {On an integral-type operator between $H^2$ space and weighted Bergman spaces},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {18},
number = {1},
year = {2011},
pages = { 63-71},
language = {en},
url = {http://dml.mathdoc.fr/item/1299766488}
}
Zhu, Xiangling. On an integral-type operator between $H^2$ space and weighted Bergman spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, pp. 63-71. http://gdmltest.u-ga.fr/item/1299766488/