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Published in:
On Some Pointwise Inequalities Involving Nonlocal Operators Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Intrinsic Difference Quotients

Author : Raul Paolo Serapioni

Published in: Harmonic Analysis, Partial Differential Equations and Applications

Publisher: Springer International Publishing

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Abstract

An alternative characterizations of intrinsic Lipschitz functions within Carnot groups through the boundedness of appropriately defined difference quotients is provided. It is also shown how intrinsic difference quotients along horizontal directions are naturally related with the intrinsic derivatives, introduced e.g. in Franchi et al. (Comm Anal Geom 11(5):909–944, 2003) and Ambrosio et al. (J Geom Anal 16:187–232, 2006) and used to characterize intrinsic real valued C 1 functions inside Heisenberg groups. Finally the question of the equivalence of the two conditions: (1) boundedness of horizontal intrinsic difference quotients and (2) intrinsic Lipschitz continuity is addressed in a few cases.

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previous chapter A Good-λ Lemma, Two Weight T1 Theorems Without Weak Boundedness, and a Two Weight Accretive Global Tb Theorem
next chapter Multilinear Weighted Norm Inequalities Under Integral Type Regularity Conditions
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Metadata
Title
Intrinsic Difference Quotients
Author
Raul Paolo Serapioni
Copyright Year
2017
Book
Harmonic Analysis, Partial Differential Equations and Applications

Print ISBN: 978-3-319-52741-3

Electronic ISBN: 978-3-319-52742-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52742-0_10

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