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...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: De Nápoli, Pablo, Rocío Díaz Martín
Format: Article
Language:English
Subjects:
Inequalities
Lie groups
Sobolev space
Online Access:Get full text
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Summary: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.
ISSN:2331-8422