arXiv subjects
Publications and source records attributed to Anca-Nicoleta Marcoci.
We prove sharp reversed Hardy-type inequalities on the cone of decreasing sequences in weighted $\ell^p$-spaces with power weights, applying them to estimate standard norms in Lorentz sequence spaces. We prove that the discrete structure of these spaces yields optimal constants that are different from those in the continuous setting.
In this article, we study some classes of solutions for a stationary Navier-Stokes equation where we consider a rough drift given by a singular integral operator which does not belong to the classical Calder{ó}n-Zygmund family of singular integral operators. Given a small external force, we will construct solutions to this system in the framework of weighted Morrey-Sobolev spaces. The use of Morrey-based Sobolev spaces provides a more general setting than the usual Lebesgue-based Sobolev spaces, and the presence of Muckenhoupt weights will allow us to present some existence and uniqueness results from several points of view.
We construct here global mild solutions in a critical setting for a class of transport-diffusion equations with a drift term that involves rough Calder{ó}n-Zygmund operators.
We establish a new pointwise estimate for a class of rough operators in the setting of metric measure spaces endowed with a measure which is Ahlfors regular. This pointwise inequality can be divided in two steps: the first one relies in a subrepresentation formula that involves a modified Riesz potential and the upper gradient of the function considered and the second step gives a pointwise control of the Riesz potential in terms of a maximal function and a Morrey norm. We also investigate a family of functional inequalities that can be deduced from this pointwise estimate.
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of weighted Sobolev-type inequalities.
We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.
The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class Bp, we will study Gagliardo-Nirenberg inequalities. As a by-product we will also consider Morrey-Sobolev inequalities. These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups.