Littlewood-Paley operators on the generalized Lipschitz spaces.
Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2
We study the weak type (1,1) and the -boundedness, 1 < p ≤ 2, of the so-called vertical (i.e. involving space derivatives) Littlewood-Paley-Stein functions and ℋ respectively associated with the Poisson semigroup and the heat semigroup on a complete Riemannian manifold M. Without any assumption on M, we observe that and ℋ are bounded in , 1 < p ≤ 2. We also consider modified Littlewood-Paley-Stein functions that take into account the positivity of the bottom of the spectrum. Assuming that...
Littlewood-Paley-Stein theory for semigroups in UMD spaces.
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.
Local estimates for Jacobi polynomials.
Local Field Singular Integrals with Complex Homogeneity.
Local integrability of strong and iterated maximal functions
Let denote the strong maximal operator. Let and denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that but . It is shown that if f is a function supported on Q such that but , then there exists a set A of finite measure in ℝ² such that .
Local means and wavelets in function spaces
The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type and on ℝⁿ and on ⁿ.
Local means and wavelets in function spaces with local Muckenhoupt weights
The paper deals with local means and wavelet bases in function spaces of Besov and Triebel-Lizorkin type with local Muckenhoupt weights.
Local properties of Fourier series.
Local Riesz transform characterization of local Hardy spaces
Local Theorems for the Absolute Convergence of Multiple Lacunary Fourier Series.
Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets
We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions , where for a fixed function ϕ, denotes the one-dimensional orthogonal projection on the function , U is a group representation and g is an element of the group. They are defined as integrals , where W is an open, relatively...
Localisation fréquentielle des paquets d'ondelettes.
Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets wn suffer a lack of frequency localization. Using the L1-norm of the Fourier transform ^wn as localization criterion, they showed that the average 2-jΣn=02j-1 ||^wn||L1 blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question,...
Localization and Convergence of Eigenfunction Expansions.
Localization and summability of multiple Hermite series.
Localization of factored Fourier series.
Localization of Spherical Harmonic Expansions.
Logarithmic inequalities for second-order Riesz transforms and related Fourier multipliers
We study logarithmic estimates for a class of Fourier multipliers which arise from a nonsymmetric modulation of jumps of Lévy processes. In particular, this leads to corresponding tight bounds for second-order Riesz transforms on .
Logarithmic Sobolev inequalitites and the existence of singular integrals.