Associated weights and spaces of holomorphic functions

Klaus Bierstedt; José Bonet; Jari Taskinen

Studia Mathematica (1998)

  • Volume: 127, Issue: 2, page 137-168
  • ISSN: 0039-3223

Abstract

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When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset G ⊂ ℂ N which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.

How to cite

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Bierstedt, Klaus, Bonet, José, and Taskinen, Jari. "Associated weights and spaces of holomorphic functions." Studia Mathematica 127.2 (1998): 137-168. <http://eudml.org/doc/216464>.

@article{Bierstedt1998,
abstract = {When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G ⊂ ℂ^N$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.},
author = {Bierstedt, Klaus, Bonet, José, Taskinen, Jari},
journal = {Studia Mathematica},
keywords = {growth function; weighted space of holomorphic functions; isometry; inductive limit; weighted (LB)-space; bounded (DFS)-property; bounded retractivity property; semi-Montel property},
language = {eng},
number = {2},
pages = {137-168},
title = {Associated weights and spaces of holomorphic functions},
url = {http://eudml.org/doc/216464},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Bierstedt, Klaus
AU - Bonet, José
AU - Taskinen, Jari
TI - Associated weights and spaces of holomorphic functions
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 2
SP - 137
EP - 168
AB - When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G ⊂ ℂ^N$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.
LA - eng
KW - growth function; weighted space of holomorphic functions; isometry; inductive limit; weighted (LB)-space; bounded (DFS)-property; bounded retractivity property; semi-Montel property
UR - http://eudml.org/doc/216464
ER -

References

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