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1
Content available remote

Essential norms of weighted composition operators on the space $ℋ^{∞}$ of Dirichlet series

100%
Lefèvre P.
Studia Mathematica
|
2009
|
tom 191
|
nr 1
57-66
EN
We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space $ℋ^{∞}$ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.
2
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Measures and lacunary sets

100%
Lefèvre P.
Studia Mathematica
|
1999
|
tom 133
|
nr 2
145-161
EN
We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
3
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Some remarks on quasi-Cohen sets

64%
Lefèvre P., Li D.
Colloquium Mathematicum
|
2001
|
tom 89
|
nr 2
169-178
EN
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection $C(G)/C_{E^{c}}(G) ↪ L²_{E}(G)$ is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.
4
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Some Banach spaces of Dirichlet series

64%
Bailleul M., Lefèvre P.
Studia Mathematica
|
2015
|
tom 226
|
nr 1
17-55
EN
The Hardy spaces of Dirichlet series, denoted by $𝓗^{p}$ (p ≥ 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general case. In this paper we study some $L^{p}$-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted $𝓐^{p}$ and $ℬ^{p}$. Each could appear as a "natural" way to generalize the classical case of the unit disk. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p = 2. Surprisingly, it appears that the two spaces have a different behavior relative to the Hardy spaces and that these behaviors are different from the usual way the Hardy spaces $H^{p}(𝔻)$ embed into Bergman spaces on the unit disk.
5
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Weak compactness and Orlicz spaces

51%
Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L.
Colloquium Mathematicum
|
2008
|
tom 112
|
nr 1
23-32
EN
We give new proofs that some Banach spaces have Pełczyński's property (V).
6
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The canonical injection of the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$

51%
Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L.
Studia Mathematica
|
2011
|
tom 202
|
nr 2
123-144
EN
We study the canonical injection from the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$.
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