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Associated weights and spaces of holomorphic functions

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Bierstedt K. D., Bonet J., Taskinen J.

Studia Mathematica

1998

tom 127

nr 2

137-168

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.

Ograniczanie wyników

1 Studia Mathematica

1 Bierstedt K. D.

1 Bonet J.

1 Taskinen J.

1 1998

Wyniki wyszukiwania

Associated weights and spaces of holomorphic functions