Carleson measures and Toeplitz operators on small Bergman spaces on the ball

Van An Le

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 211-229
  • ISSN: 0011-4642

Abstract

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We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip’s results from the unit disk of ℂ to the unit ball of ℂ n . We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1 < p < ∞ .

How to cite

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Le, Van An. "Carleson measures and Toeplitz operators on small Bergman spaces on the ball." Czechoslovak Mathematical Journal (2021): 211-229. <http://eudml.org/doc/297295>.

@article{Le2021,
abstract = {We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip’s results from the unit disk of $\mathbb \{C\}$ to the unit ball of $\mathbb \{C\}^n$. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten $p$ classes membership of Toeplitz operators for $1<p<\infty $.},
author = {Le, Van An},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bergman space; Carleson measure; Toeplitz operator; Schatten classes},
language = {eng},
number = {1},
pages = {211-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Carleson measures and Toeplitz operators on small Bergman spaces on the ball},
url = {http://eudml.org/doc/297295},
year = {2021},
}

TY - JOUR
AU - Le, Van An
TI - Carleson measures and Toeplitz operators on small Bergman spaces on the ball
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 211
EP - 229
AB - We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip’s results from the unit disk of $\mathbb {C}$ to the unit ball of $\mathbb {C}^n$. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten $p$ classes membership of Toeplitz operators for $1<p<\infty $.
LA - eng
KW - Bergman space; Carleson measure; Toeplitz operator; Schatten classes
UR - http://eudml.org/doc/297295
ER -

References

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