Techniques probabilistes pour l'étude de problèmes d'isomorphismes entre espaces de Banach
Tensor product in symmetric function spaces.
A concept of the multiplicator of symmetric function space concerning to projective tensor product is introduced and studied. This allows us to obtain some concrete results. In particular, the well-know theorem of R. O'Neil about boundedness of tensor product in the Lorentz spaces Lpq is discussed.
The Banach-Saks property in rearrangement invariant spaces
This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the...
The basis properties of power systems in .
The Bergman projection on weighted spaces: L¹ and Herz spaces
We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces .
The best L2-approximation by finite sums of functions with separable variables.
The bilinear maximal functions map into for .
The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.
The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent
The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.
The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or Hölder spaces...
The canonical injection of the Hardy-Orlicz space into the Bergman-Orlicz space
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
The canonical seminorm on Weak L¹
The class Bpfor weighted generalized Fourier transform inequalities
In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.
The class of convolution operators on the Marcinkiewicz spaces
Let denote the operator-norm closure of the class of convolution operators where is a suitable function space on . Let be the closed subspace of regular functions in the Marinkiewicz space , . We show that the space is isometrically isomorphic to and that strong operator sequential convergence and norm convergence in coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on .
The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces
The completely continuous property in Orlicz spaces.
We show that in Orlicz spaces equipped with Luxemburg norm and Orlicz norm, the RNP, CCP, PCP and CPCP are equivalent.
The continuity of the rearrangement in
The converse of the Hölder inequality and its generalizations
Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist...
The coordinatewise uniformly Kadec-Klee property in some Banach spaces.
The criteria for local uniform rotundity of Orlicz spaces