Compact differences of composition operators on weighted Dirichlet spaces

Robert Allen; Katherine Heller; Matthew Pons

Open Mathematics (2014)

  • Volume: 12, Issue: 7, page 1040-1051
  • ISSN: 2391-5455

Abstract

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Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

How to cite

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Robert Allen, Katherine Heller, and Matthew Pons. "Compact differences of composition operators on weighted Dirichlet spaces." Open Mathematics 12.7 (2014): 1040-1051. <http://eudml.org/doc/269467>.

@article{RobertAllen2014,
abstract = {Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.},
author = {Robert Allen, Katherine Heller, Matthew Pons},
journal = {Open Mathematics},
keywords = {Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation; composition operator; compact difference; weighted Dirichlet space; complex interpolation},
language = {eng},
number = {7},
pages = {1040-1051},
title = {Compact differences of composition operators on weighted Dirichlet spaces},
url = {http://eudml.org/doc/269467},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Robert Allen
AU - Katherine Heller
AU - Matthew Pons
TI - Compact differences of composition operators on weighted Dirichlet spaces
JO - Open Mathematics
PY - 2014
VL - 12
IS - 7
SP - 1040
EP - 1051
AB - Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.
LA - eng
KW - Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation; composition operator; compact difference; weighted Dirichlet space; complex interpolation
UR - http://eudml.org/doc/269467
ER -

References

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