Boundary vs. interior conditions associated with weighted composition operators

Kei Izuchi; Yuko Izuchi; Shûichi Ohno

Open Mathematics (2014)

  • Volume: 12, Issue: 5, page 761-777
  • ISSN: 2391-5455

Abstract

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Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk 𝔻 , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior 𝔻 and on the boundary ∂ 𝔻 respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

How to cite

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Kei Izuchi, Yuko Izuchi, and Shûichi Ohno. "Boundary vs. interior conditions associated with weighted composition operators." Open Mathematics 12.5 (2014): 761-777. <http://eudml.org/doc/268969>.

@article{KeiIzuchi2014,
abstract = {Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk \[\mathbb \{D\}\] , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior \[\mathbb \{D\}\] and on the boundary \[\partial \mathbb \{D\}\] respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.},
author = {Kei Izuchi, Yuko Izuchi, Shûichi Ohno},
journal = {Open Mathematics},
keywords = {Weighted composition operator; The space of bounded harmonic functions; The space of bounded analytic functions; Essential norm; weighted composition operator; space of bounded harmonic functions; space of bounded analytic functions; essential norm},
language = {eng},
number = {5},
pages = {761-777},
title = {Boundary vs. interior conditions associated with weighted composition operators},
url = {http://eudml.org/doc/268969},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Kei Izuchi
AU - Yuko Izuchi
AU - Shûichi Ohno
TI - Boundary vs. interior conditions associated with weighted composition operators
JO - Open Mathematics
PY - 2014
VL - 12
IS - 5
SP - 761
EP - 777
AB - Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk \[\mathbb {D}\] , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior \[\mathbb {D}\] and on the boundary \[\partial \mathbb {D}\] respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.
LA - eng
KW - Weighted composition operator; The space of bounded harmonic functions; The space of bounded analytic functions; Essential norm; weighted composition operator; space of bounded harmonic functions; space of bounded analytic functions; essential norm
UR - http://eudml.org/doc/268969
ER -

References

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