BOUNDEDNESS OF BEREZIN TRANSFORM ON HERZ SPACES

Title & Authors
BOUNDEDNESS OF BEREZIN TRANSFORM ON HERZ SPACES
Cho, Chu-Hee; Na, Kyun-Guk;

Abstract
In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of $\small{\mathbb{C}^n}$. And we provide the integral estimates concerning pluriharmonic kernel functions. Using this, we finally obtain the growth estimates of the Berezin transforms on such Herz spaces.
Keywords
Berezin transform;Schatten space;Herz space;
Language
English
Cited by
References
1.
B. R. Choe, Note on the Berezin transform on Herz spaces, RIMS Kyokuroku 1519 (2006), 21-37.

2.
B. R. Choe, H. Koo, and K. Na, Positive Toeplitz operators of Schatten-Herz type, Nagoya Math. J. 185 (2007), 31-62.

3.
M. Loaiza, M. Lopez-Garcia, and S. Perez-Esteva, Herz classes and Toeplitz operators in the disk, Integral Equations Operator Theory 53 (2005), no. 2, 287-296.

4.
K. Na, Positive Schatten(-Herz) class Toeplitz operators on pluriharmonic Bergman spaces, Integral Equations Operator Theory 64 (2009), no. 3, 409-428.

5.
W. Rudin, Function Theory in the Unit Ball of \$C^n\$, Springer Verlag, 1980.