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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.

Order bounded composition operators on the Hardy spaces and the Nevanlinna class

75%

Jaoua N.

Studia Mathematica

1999

tom 134

nr 1

35-55

We study the order boundedness of composition operators induced by holomorphic self-maps of the open unit disc D. We consider these operators first on the Hardy spaces $H^p$ 0 < p < ∞ and then on the Nevanlinna class N. Given a non-negative increasing function h on [0,∞[, a composition operator is said to be X,L_h-order bounded (we write (X,L_h)-ob) with $X = H^p$ or X = N if its composition with the map f ↦ f*, where f* denotes the radial limit of f, is order bounded from X into $L_h$. We give a complete characterization and a family of examples in both cases. On the other hand, we show that the ($N,log^{+}L$)-ob composition operators are exactly those which are Hilbert-Schmidt on $H^2$. We also prove that the ($N,L^q$)-ob composition operators are exactly those which are compact from N into $H^q$.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

1 Iida Y.

1 Jaoua N.

1 Takahashi K.

1 2013

1 1999

Wyniki wyszukiwania

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

Order bounded composition operators on the Hardy spaces and the Nevanlinna class