A weighted norm inequality for singular integrals
A Weighted Tauberian Theorem.
A weighted vector-valued weak type (1,1) inequality and spherical summation
We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.
A weighted version of Journé's lemma.
In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R2 where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces Hu'p (R+2 x R+2) and a description of their duals when p is close to 1.
A₁-regularity and boundedness of Calderón-Zygmund operators
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...
Abelova cena v roce 2017 udělena za teorii waveletů
Abelovu cenu za matematiku získal v roce 2017 francouzský matematik Yves Meyer za rozvoj teorie waveletů. V článku se seznámíme s jeho vědeckým životopisem, hlavní myšlenkou teorie waveletů a jejich použitím v praxi.
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.
About Certain Singular Kernels K(x,y) = K1(x-y)K2(x+y).
About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system.
About Riesz transforms on the Heisenberg groups.
About the Lp-Boundedness of Integral Operators with Kernels of the Form K1 (x-y)K2(x+y).
Absolute continuity for elliptic-caloric measures
A Carleson condition on the difference function for the coefficients of two elliptic-caloric operators is shown to give absolute continuity of one measure with respect to the other on the lateral boundary. The elliptic operators can have time dependent coefficients and only one of them is assumed to have a measure which is doubling. This theorem is an extension of a result of B. Dahlberg [4] on absolute continuity for elliptic measures to the case of the heat equation. The method of proof is an...
Absolute convergence of Fourier series of a function of Wiener’s class
Absolute convergence of Fourier series on finite-dimensional groups
Absolute convergence of multiple Fourier integrals
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
Absolute convergence of the double series of Fourier-Haar coefficients.
Absolute Nörlund summability factors of power series and Fourier series
Four theorems of Ahmad [1] on absolute Nörlund summability factors of power series and Fourier series are proved under weaker conditions.
Absolute Nörlund summability factors of power series and Fourier series
Absolute Riesz summability of Fourier series
Absolutely convergent Fourier series and generalized Lipschitz classes of functions
We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if for all x ∈ , h >...