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Isometries of some F-algebras of holomorphic functions on the upper half plane

100%

Iida Y., Takahashi K.

Open Mathematics

2013

tom 11

nr 6

1034-1038

Linear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.

Thin sequences in the corona of H ∞

76%

Stankov D., Tzonev T.

Open Mathematics

2013

tom 11

nr 10

1843-1849

In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^\infty )\backslash \mathbb{D}$$ of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

Ograniczanie wyników

2 Open Mathematics

1 Iida Y.

1 Stankov D.

1 Takahashi K.

1 Tzonev T.

2 2013

Wyniki wyszukiwania

Isometries of some F-algebras of holomorphic functions on the upper half plane

Thin sequences in the corona of H ∞