- Tytuł:
- Order bounded composition operators on the Hardy spaces and the Nevanlinna class
- Autorzy:
- Jaoua, Nizar
- Powiązania:
- https://bibliotekanauki.pl/articles/1217094.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
composition operators
order bounded maps
Hardy spaces
Nevanlinna class
radial limit
moment sequences and analytic moment sequences - Opis:
- 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 $H^q$.
- Źródło:
-
Studia Mathematica; 1999, 134, 1; 35-55
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł