Positive Toeplitz operators between the pluriharmonic Bergman spaces

Eun Sun Choi

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 1, page 93-111
  • ISSN: 0011-4642

Abstract

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We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b p into another b q for 1 < p , q < ∞ in terms of certain Carleson and vanishing Carleson measures.

How to cite

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Choi, Eun Sun. "Positive Toeplitz operators between the pluriharmonic Bergman spaces." Czechoslovak Mathematical Journal 58.1 (2008): 93-111. <http://eudml.org/doc/31201>.

@article{Choi2008,
abstract = {We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space $b^p$ into another $b^q$ for $1 < p, q < \infty $ in terms of certain Carleson and vanishing Carleson measures.},
author = {Choi, Eun Sun},
journal = {Czechoslovak Mathematical Journal},
keywords = {Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure; Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure},
language = {eng},
number = {1},
pages = {93-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive Toeplitz operators between the pluriharmonic Bergman spaces},
url = {http://eudml.org/doc/31201},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Choi, Eun Sun
TI - Positive Toeplitz operators between the pluriharmonic Bergman spaces
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 93
EP - 111
AB - We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space $b^p$ into another $b^q$ for $1 < p, q < \infty $ in terms of certain Carleson and vanishing Carleson measures.
LA - eng
KW - Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure; Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure
UR - http://eudml.org/doc/31201
ER -

References

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  1. 10.1023/A:1016356229211, Potential Anal. 17 (2002), 307–335. (2002) MR1918239DOI10.1023/A:1016356229211
  2. 10.2748/tmj/1113246553, Tohoku Math.  J. 56 (2004), 255–270. (2004) MR2053321DOI10.2748/tmj/1113246553
  3. 10.1215/kjm/1250281046, J. Math. Kyoto Univ. 47 (2007), 247–267. (2007) Zbl1158.32001MR2376957DOI10.1215/kjm/1250281046
  4. 10.1307/mmj/1029004756, Mich. Math.  J. 40 (1993), 333–358. (1993) MR1226835DOI10.1307/mmj/1029004756
  5. 10.1007/BF01192123, Integral Equations Oper. Theory 27 (1997), 426–438. (1997) Zbl0902.47026MR1442127DOI10.1007/BF01192123
  6. Operator Theory in Function Spaces, Marcell Dekker, New York, 1990. (1990) Zbl0706.47019MR1074007
  7. Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J.  Oper. Theory 20 (1988), 329–357. (1988) Zbl0676.47016MR1004127
  8. Function Theory in the Unit Ball of  ℂ n , Springer-Verlag, New York, 1980. (1980) MR0601594

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