Examples of singular maximal functions unbounded on Lp.
Examples of Λ(4) sets E and a graph structure in E x E
Existence globale pour un fluide inhomogène
Dans cet article on s’intéresse à l’existence et l’unicité globale de solutions pour le système de Navier-Stokes à densité variable, lorsque la donnée initiale de la vitesse est dans l’espace de Besov homogène de régularité critique . Notons que ce résultat fait suite aux résultats de H. Abidi qui a généralisé le travail de R. Danchin. Toutefois, dans les travaux antérieurs, l’existence de la solution est obtenue pour et l’unicité est démontrée sous l’hypothèse plus restrictive Notre résultat...
Exponential integrability of certain singular integral transforms
Extensions of Fatou Theorems in Products of Upper Half-Spaces.
Extensions of Rubio de Francia's extrapolation theorem.
One of the main results in modern harmonic analysis is the extrapolation theorem of J. L. Rubio de Francia for Ap weights. In this paper we discuss some recent extensions of this result. We present a new approach that, among other things, allows us to obtain estimates in rearrangement-invariant Banach function spaces as well as weighted modular inequalities. We also extend this extrapolation technique to the context of A∞ weights. We apply the obtained results to the dyadic square function. Fractional...
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces.
Factorization and extrapolation of pairs of weights
Factorization theorem for product Hardy spaces
We extend the well known factorization theorems on the unit disk to product Hardy spaces, which generalizes the previous results obtained by Coifman, Rochberg and Weiss. The basic tools are the boundedness of a certain bilinear form on ℝ²₊ × ℝ²₊ and the characterization of BMO(ℝ²₊ × ℝ²₊) recently obtained by Ferguson, Lacey and Sadosky.
Fixed points of the Hardy-Littlewood maximal operator.
Fluides légèrement compressibles et limite incompressible
Fourier analysis in several parameters.
Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on Rn [1].
Fourier series and the maximal operator on the weighted special atom spaces.
Fractional Hajłasz-Morrey-Sobolev spaces on quasi-metric measure spaces
In this article, via fractional Hajłasz gradients, the authors introduce a class of fractional Hajłasz-Morrey-Sobolev spaces, and investigate the relations among these spaces, (grand) Morrey-Triebel-Lizorkin spaces and Triebel-Lizorkin-type spaces on both Euclidean spaces and RD-spaces.
Fractional integrals on spaces of homogeneous type
Fractional integration on the space and its dual
Fractional Maximal Functions in Metric Measure Spaces
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Frames associated with expansive matrix dilations.
We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.
Function algebras of Besov and Triebel-Lizorkin-type
We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
Gabor meets Littlewood-Paley: Gabor expansions in
It is known that Gabor expansions do not converge unconditionally in and that cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in -norm.