BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL
2015 ◽
Vol 99
(2)
◽
pp. 237-249
Keyword(s):
Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.
Keyword(s):
2000 ◽
Vol 42
(1)
◽
pp. 31-35
◽
2009 ◽
Vol 7
(3)
◽
pp. 225-240
◽
2008 ◽
Vol 19
(06)
◽
pp. 645-669
◽
2010 ◽
Vol 89
(3)
◽
pp. 407-418
◽
2013 ◽
Vol 2013
◽
pp. 1-5
◽
Keyword(s):