Translating Inequalities between Hardy and Bergman Spaces

2004 ◽  
Vol 111 (6) ◽  
pp. 520 ◽  
Author(s):  
Kehe Zhu
Keyword(s):  
Bergman Spaces ◽  
Hardy And Bergman Spaces

scholarly journals Monsters in Hardy and Bergman Spaces

2002 ◽  
Vol 47 (5) ◽  
pp. 373-382 ◽  
Author(s):  
L. Bernal-González ◽  
M.C. Calderón-Moreno
Keyword(s):  
Bergman Spaces ◽  
Hardy And Bergman Spaces

Cesàro-Like Operators on the Hardy and Bergman Spaces of the Half Plane

2015 ◽  
Vol 10 (1) ◽  
pp. 187-203 ◽  
Author(s):  
S. Ballamoole ◽  
J. O. Bonyo ◽  
T. L. Miller ◽  
V. G. Miller
Keyword(s):  
Half Plane ◽  
Bergman Spaces ◽  
Hardy And Bergman Spaces

scholarly journals Toeplitz operators on generalized Bergman-Hardy spaces

2001 ◽  
Vol 88 (1) ◽  
pp. 96
Author(s):  
Wolfgang Lusky
Keyword(s):  
Hardy Spaces ◽  
Toeplitz Operators ◽  
Fock Space ◽  
Bergman Spaces ◽  
Trigonometric Polynomials ◽  
Essential Spectra ◽  
Radial Functions ◽  
Hardy And Bergman Spaces ◽  
Schmidt Operator ◽  
Vector Valued

We study the Toeplitz operators $T_f: H_2 \to H_2$, for $f \in L_\infty$, on a class of spaces $H_2$ which in- cludes, among many other examples, the Hardy and Bergman spaces as well as the Fock space. We investigate the space $X$ of those elements $f \in L_\infty$ with $\lim_j \|T_f-T_{f_j}\|=0$ where $(f_j)$ is a sequence of vector-valued trigonometric polynomials whose coefficients are radial functions. For these $T_f$ we obtain explicit descriptions of their essential spectra. Moreover, we show that $f \in X$, whenever $T_f$ is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those $f \in L_\infty$ where $T_f$ is a Hilbert-Schmidt operator.

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