Now showing items 1-20 of 23

    • IconA criterion of weak compactness for operators on subspaces of Orlicz spaces  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Hindawi, 2008)
      We give a criterion of weak compactness for the operators on the Morse-Transue space MΨ , the subspace of the Orlicz space LΨ generated by L∞.
    • IconA spectral radius type formula for approximation numbers of composition operators  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Elsevier, 2014-12-15)
      For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞⁡[an(Cφ)]1/n=e−1 ...
    • IconApproximation numbers of composition operators on Hp  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (De Gruyter Open, 2015-01)
      We give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞.
    • IconApproximation numbers of composition operators on the Dirichlet space  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2015-04)
      We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of O. El-Fallah, K. Kellay, M. ...
    • IconApproximation numbers of composition operators on the Hardy space of the infinite polydisk  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2017-12)
      We study the composition operators of the Hardy space on D∞ ∩ℓ1, the ℓ1 part of the infinite polydisk, and the behavior of their approximation numbers.
    • IconApproximation numbers of weighted composition operators  [Article]

      Lechner, Gandalf; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Elsevier, 2018)
      We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers ...
    • IconCompact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2011-09)
      We construct an analytic self-map ϕ of the unit disk and an Orlicz function Ψ for which the composition operator of symbol ϕ is compact on the Hardy-Orlicz space HΨ, but not on the Bergman-Orlicz space BΨ. For that, we first ...
    • IconCompact composition operators on the Dirichlet space and capacity of sets of contact points  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Elsevier, 2013-02-15)
      We prove several results about composition operators on the Dirichlet space D⁎. For every compact set K⊆∂D of logarithmic capacity , there exists a Schur function φ both in the disk algebra A(D) and in D⁎ such that the ...
    • IconComposition operators on Hardy-Orlicz spaces  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (American Mathematical Society, 2010)
      We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Ψ grows rapidly: compactness, weak compactness, to be p-summing, order bounded,..., and show how these notions behave according to the ...
    • IconEstimates for approximation numbers of some classes of composition operators on the Hardy space  [Article]

      Rodríguez Piazza, Luis; Li, Daniel; Queffélec, Hervé (2013)
    • IconInfinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2013-08)
      We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(z), where A is the normalized area measure on the unit disk D, by every analytic self-map φ:D→D is not only an (α+2)-Carleson ...
    • IconNevanlinna counting function and Carleson function of analytic maps  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2011-10)
      We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.
    • IconOn approximation numbers of composition operators  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Elsevier, 2012-04)
      We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at ...
    • IconOn some random thin sets of integers  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (American Mathematical Society, 2008-01)
      We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in Some new thin ...
    • IconSome examples of compact composition operators on H2  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Elsevier, 2008-12-01)
      We construct, in an essentially explicit way, various composition operators on H2 and study their compactness or their membership in the Schatten classes. We construct: non-compact composition operators on H2 whose symbols ...
    • IconSome new properties of composition operators associated with lens maps  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2013-05)
      We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H2. The last ones are connected with ...
    • IconSome new thin sets of integers in harmonic analysis  [Article]

      Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Springer, 2002-12)
      We randomly construct various subsets A of the integers which have both smallness and largeness properties. They are small since they are very close, in various senses, to Sidon sets: the continuous functions with spectrum ...
    • IconSome revisited results about composition operators on Hardy spaces  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (European Mathematical Society, 2012)
      We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on ...
    • IconSome translation-invariant Banach function spaces which contain C0  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Polish Academy of Sciences, Institute of Mathematics, 2004)
      We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c0.
    • IconThe canonical injection of the Hardy-Orlicz space HΨ into the Bergman–Orlicz space BΨ  [Article]

      Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis (Polish Academy of Sciences, Institute of Mathematics, 2011)
      We study the canonical injection from the Hardy-Orlicz space HΨ into the Bergman–Orlicz space BΨ..