Abstract
In Carnot-Carathéodory metric spaces related to a family of free Hörmander vector fields X 1,...,X q, we prove that the space C ∞ is locally dense in VMO ω with respect to BMO ω norm.
Key words
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Acquistapace, On BMO regularity for linear elliptic systems, Ann. Mat. Pura Appl., (4) 161 (1992) 231–269.
M. Bramanti and L. Brandolini, Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDES, to appear on Revista Matematica Iberoamericana.
A.O. Caruso, Interior S 1,pX,loc estimates for variational hypoelliptic operators with coefficients locally in VMO X, preprint (2003).
A.O. Caruso and M.S. Fanciullo, BMO on spaces of homogeneous type: a density result, preprint (2003).
F. Chiarenza, M. Frasca and P. Longo, W 2,p — solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 336,1, (1993), 841–853.
M. Christ, Lectures on singular integral operators, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics, 77 (1990).
M. Christ, A T(b) Theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math., LX/LXI,2, (1990), 601–628.
R. Coifman and G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogenes, Lectures Notes in Mathematics, 242, Springer-Verlag (1971).
G. Di Fazio, L p estimates for Divergence Form Elliptic Equations with Discontinuous Coefficients, Boll. U.M.I. (7) 10-A, (1996), 409–420.
G. Di Fazio and M.S. Fanciullo, BMO regularity for elliptic systems in Carnot-Carathéodory spaces, Comm. on Applied Nonlinear Analysis, 10 (2003), n.2, 81–95
M. Gromov, Carnot-Carathéodory spaces seen from within, in Sub-Riemannian Geometry, Progress in Mathematics 144, ed. by A. Bellaïche and J. Risler, Birkhäuser (1996).
L.P. Rothschild and E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math., 137 (1976), 247–320.
D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc., 207 (1975), 391–405.
S. Spanne, Some functions spaces defined using the mean oscillation over cubes, Ann. Sc. Norm. Sup. Pisa (3), 19 (1965), 593–608.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Caruso, A.O., Fanciullo, M.S. (2005). A Density Result on the Space VMO ω . In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_17
Download citation
DOI: https://doi.org/10.1007/0-387-24276-7_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24209-5
Online ISBN: 978-0-387-24276-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)