Toeplitz operators on Bergman spaces and Hardy multipliers

Wolfgang Lusky, and Jari Taskinen. "Toeplitz operators on Bergman spaces and Hardy multipliers." Studia Mathematica 204.2 (2011): 137-154. <http://eudml.org/doc/285518>.

@article{WolfgangLusky2011,
abstract = {We study Toeplitz operators $T_\{a\}$ with radial symbols in weighted Bergman spaces $A_\{μ\}^\{p\}$, 1 < p < ∞, on the disc. Using a decomposition of $A_\{μ\}^\{p\}$ into finite-dimensional subspaces the operator $T_\{a\}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_\{a\}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_\{a\}$ for a satisfying an assumption on the positivity of certain indefinite integrals.},
author = {Wolfgang Lusky, Jari Taskinen},
journal = {Studia Mathematica},
keywords = {Toeplitz operator; weighted Bergman space; radial symbol; radial weight},
language = {eng},
number = {2},
pages = {137-154},
title = {Toeplitz operators on Bergman spaces and Hardy multipliers},
url = {http://eudml.org/doc/285518},
volume = {204},
year = {2011},
}

TY - JOUR
AU - Wolfgang Lusky
AU - Jari Taskinen
TI - Toeplitz operators on Bergman spaces and Hardy multipliers
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 2
SP - 137
EP - 154
AB - We study Toeplitz operators $T_{a}$ with radial symbols in weighted Bergman spaces $A_{μ}^{p}$, 1 < p < ∞, on the disc. Using a decomposition of $A_{μ}^{p}$ into finite-dimensional subspaces the operator $T_{a}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_{a}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_{a}$ for a satisfying an assumption on the positivity of certain indefinite integrals.
LA - eng
KW - Toeplitz operator; weighted Bergman space; radial symbol; radial weight
UR - http://eudml.org/doc/285518
ER -