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

Studia Mathematica (1999)

- Volume: 134, Issue: 1, page 35-55
- ISSN: 0039-3223

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topJaoua, Nizar. "Order bounded composition operators on the Hardy spaces and the Nevanlinna class." Studia Mathematica 134.1 (1999): 35-55. <http://eudml.org/doc/216621>.

@article{Jaoua1999,

abstract = {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,Lh-order bounded (we write (X,Lh)-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 $H^q$.},

author = {Jaoua, Nizar},

journal = {Studia Mathematica},

keywords = {composition operators; order bounded maps; Hardy spaces; Nevanlinna class; radial limit; moment sequences and analytic moment sequences; composition operator; boundedness},

language = {eng},

number = {1},

pages = {35-55},

title = {Order bounded composition operators on the Hardy spaces and the Nevanlinna class},

url = {http://eudml.org/doc/216621},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Jaoua, Nizar

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

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 1

SP - 35

EP - 55

AB - 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,Lh-order bounded (we write (X,Lh)-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 $H^q$.

LA - eng

KW - composition operators; order bounded maps; Hardy spaces; Nevanlinna class; radial limit; moment sequences and analytic moment sequences; composition operator; boundedness

UR - http://eudml.org/doc/216621

ER -

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