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arXiv · 2109.05064

Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups

Pablo De Nápoli·Rocío Díaz Martín
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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 $L^p$-spaces and by considering second-order differences.

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Pablo De Nápoli, Rocío Díaz Martín. 2021-09-10. Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups. https://arxiv.org/abs/2109.05064

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