Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups
Abstract
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 -spaces and by considering second-order differences.
Keywords
Cite
@article{arxiv.2109.05064,
title = {Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups},
author = {Pablo De Nápoli and Rocío Díaz Martín},
journal= {arXiv preprint arXiv:2109.05064},
year = {2023}
}
Comments
We extended the abstract. We corrected a definition of Sobolev spaces defined by derivatives $\mathbb{W}_{p;k}(\mathbb{G})$ on page 1 (suitable for Theorem 3.6). We added the corresponding reference [R Burns. "Sobolev spaces on Lie groups". PhD thesis. The Australian National University, 1991. The definition of inhomogeneous Sobolev spaces of potential type remains the same