# 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

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topKei 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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