We prove estimates of Calderón-Zygmund type for evolutionary pLaplacian systems in the setting of Lorentz spaces. We suppose the coefficients of the system to satisfy only a VMO condition with respect to the space variable. Our results hold true, mutatis mutandis, also for stationary p-Laplacian systems. PUBLISHED IN J. Differential Equations 255 (9): 2927–2951, 2013

We survey on some recent results concerning weak and strong weighted L estimates for Calderón-Zygmund operators with sharp bounds when the weight satisfies the A1 condition. These questions are related to a problem posed by Muckenhoupt and Wheeden in the seventies.

Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted s...

Let (X,μ) be a non-homogeneous space in the sense that X is a metric space equipped with an upper doubling measure μ. The aim of this paper is to study the endpoint estimate of the maximal operator associated to a Calderón-Zygmund operator T and the L boundedness of the maximal commutator with RBMO functions

Let g be a holomorphic function of the unit ball B in the ndimensional space, and denote by Tg and Ig the induced extended Cesáro operator and another integral operator. The boundedness and compactness of Tg and Ig acting on the Zygmund spaces in the unit ball are discussed and necessary and sufficient conditions are given in this paper.

The aim of this paper is to prove a generalization of a well-known convexity theorem of M. Riesz [8]. The Riesz theorem was originally deduced by "real-variable" techniques. Later, Thorin [10], Tamarkin and Zygmund [9], and Thorin [ll] introduced convexity properties of analytic functions in their study of Riesz's theorem. These ideas were put in especially suggestive form by A. P. Calderon and...

Nikol’skii-type inequalities for entire functions of exponential type on $${\mathbb{R}}^{n}$$ the Lorentz–Zygmund spaces are obtained. Some new limiting cases examined. Application to Besov–type logarithmic smoothness is given.

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.

In this paper we characterize those functions f of the real line to itself such that the nonlinear superposition operator Tf defined by Tf [g] := f◦g maps the Hölder-Zygmund space Cs(Rn) to itself, is continuous, and is r times continuously differentiable. Our characterizations cover all cases in which s is real and s > 0, and seem to be novel when s > 0 is an integer.

New existence and regularity results are given for non-linear elliptic problems with measure data. The gradient of the solution is itself in an optimal (fractional) Sobolev space: this can be considered an extension of CalderónZygmund theory to measure data problems. To cite this article: G. Mingione, C. R. Acad. Sci. Paris, Ser. I.