We complete the theory of velocity averaging lemmas for transport equations by studying the limiting case of a full space derivative in the source term. Although the compactness of averages does not hold any longer, a speciic estimate remains, which shows compactness of averages in more general situations than those previously known. Our method is based on Calderon-Zygmund theory. R esum e Nous...

In the present paper, we obtain results on degree of convergence a function Fourier series in generalized Zygmund space using Karamata-Matrix (KλA) product operator. We also study an application our main result.

This paper studies the boundedness and compactness of an integraltype operator from mixed norm spaces to Zygmund-type spaces and little Zygmund-type spaces.

David and Journé discovered a criterion for the continuity on L of CalderónZygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally Hölder continuous outside the diagonal. The aim of this paper is to prove a David-Journé theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an al...

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities subspaces polynomials. focus on Hardy space Bergman one variable because they provide two settings with a strikingly different behavior.

Let μ be a non-negative Radon measure on R which only satisfies the polynomial growth condition. Let Y be a Banach space and H(μ) the Hardy space of Tolsa. In this paper, the authors prove that a linear operator T is bounded from H(μ) to Y if and only if T maps all (p, γ)-atomic blocks into uniformly bounded elements of Y; moreover, the authors prove that for a sublinear operator T bounded from...

We consider generalized Morrey spaces Mp,ω R with a general function ω x, r defining the Morrey-type norm. We find the conditions on the pair ω1, ω2 which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 R to another Mp,ω2 R , 1 < p < ∞, and from the space M1,ω1 R to the weak space WM1,ω2 R . We also prove a...

Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural an...

A holomorphic self-map φ of the unit disk is constructed such that the composition operator induced by φ is bounded on the Hardy-Sobolev space H1 2 of order 2 as well as on the ordinary holomorphic Lipschitz space Lip1 but unbounded on the Zygmund class Λ1. Among these three function spaces we have embedding relations H1 2 ⊂ Lip1 ⊂ Λ1. So, the main points here are that our construction provides...