Transformation de Riesz pour les semi-groupes symétriques. Première partie : étude de la dimension 1
Transformation de Riesz pour les semi-groupes symétriques. Seconde partie : étude sous la condition
Transformations de Marcel Riesz
Transformée de Fourier et stabilité sur les surfaces abéliennes
Translation averages of dyadic weights are not always good weights.
The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights,...
Translation invariant operators on Hardy spaces over Vilenkin groups.
Translation invariant operators on Lorentz spaces
Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1
We study convolution operators bounded on the non-normable Lorentz spaces of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...
Transmission of convergence
If , we examine the type of convergence of to so that , , implies .
Tree martingales and a.e. convergence of Vilenkin-Fourier series.
Triebel-Lizorkin spaces for Hermite expansions
This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.
Triebel-Lizorkin spaces on spaces of homogeneous type
In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].
Triebel-Lizorkin spaces with non-doubling measures
Suppose that μ is a Radon measure on , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...
Trigonometric series with -monotone coefficients in spaces with mixed quasinorm.
Triple Hilbert transforms along polynomial surfaces in .
Twisted convolutions with Calderón-Zygmund kernels.
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Two endpoint bounds for generalized Radon transforms in the plane.
Two problems associated with convex finite type domains.
We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp Lp estimates for p > 4, generalizing the Carleson-Sjölin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.
Two problems on doubling measures.
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?