Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields

Daniele Morbidelli

Studia Mathematica (2000)

  • Volume: 139, Issue: 3, page 213-244
  • ISSN: 0039-3223

Abstract

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We study the notion of fractional L p -differentiability of order s ∈ ( 0 , 1 ) along vector fields satisfying the Hörmander condition on ℝ n . We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different W s , p -norms are equivalent. We also prove a local embedding W 1 , p ⊂ W s , q , where q is a suitable exponent greater than p.

How to cite

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Morbidelli, Daniele. "Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields." Studia Mathematica 139.3 (2000): 213-244. <http://eudml.org/doc/216720>.

@article{Morbidelli2000,
abstract = {We study the notion of fractional $L^p$-differentiability of order $s∈(0,1)$ along vector fields satisfying the Hörmander condition on $ℝ^n$. We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different $W^\{s,p\}$-norms are equivalent. We also prove a local embedding $W^\{1,p\} ⊂ W^\{s,q\}$, where q is a suitable exponent greater than p.},
author = {Morbidelli, Daniele},
journal = {Studia Mathematica},
keywords = {fractional -differentiability; Carnot-Carathéodory balls; Hörmander condition; equivalent norms},
language = {eng},
number = {3},
pages = {213-244},
title = {Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields},
url = {http://eudml.org/doc/216720},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Morbidelli, Daniele
TI - Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 3
SP - 213
EP - 244
AB - We study the notion of fractional $L^p$-differentiability of order $s∈(0,1)$ along vector fields satisfying the Hörmander condition on $ℝ^n$. We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different $W^{s,p}$-norms are equivalent. We also prove a local embedding $W^{1,p} ⊂ W^{s,q}$, where q is a suitable exponent greater than p.
LA - eng
KW - fractional -differentiability; Carnot-Carathéodory balls; Hörmander condition; equivalent norms
UR - http://eudml.org/doc/216720
ER -

References

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