arXiv subjects

Pablo De Nápoli

Publications and source records attributed to Pablo De Nápoli.

3 recordsLinked to original sources

arXiv2023

Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups

We develop characterizations for Sobolev spaces of potential type on graded Lie groups, by means of Littlewood-Paley square functions, and Strichartz functionals involving second-order differences. A key role is played by some mean value inequalities that may be of independent interest. Indeed, the point-wise first-order inequality is generalized in two directions: on $L^p$-spaces and by considering second-order differences.

math.FA↗

arXiv2020

Stein-Weiss inequality in $L^{1}$ norm for vector fields

In this work, we investigate the limit case $p=1$ of the classical Stein--Weiss inequality for the Riesz potential.We present a characterization for a special class of vector fields associated to cocanceling operators introduced by Van Schaftingen in arXiv:1104.0192. As an application, we recover some div-curl inequalities found in the literature. In addition, we discuss a two-weight inequality with general weights in the scalar case, extending the previous result of Sawyer to this case.

math.CA↗

arXiv2018

Weighted Inequalities for the Fractional Laplacian and the Existence of Extremals

In this article we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein-Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of E. Lieb.

math.AP↗