Abstract
We give a short proof of Stein’s universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M.G. Cowling, On Littlewood-Paley-Stein Theory. Proceedings of the Seminar on Harmonic Analysis (Pisa, 1980), 1981
R.R. Coifman, R. Rochberg, G. Weiss, Applications of Transference: The L p Version of von Neumann’s Inequality and the Littlewood-Paley-Stein Theory. Linear Spaces and Approximation (Birkhäuser, Basel, 1978)
R.R. Coifman, G. Weiss, Transference Methods in Analysis (American Mathematical Society, Providence, 1976)
G.E. Karadzhov, M. Milman, Extrapolation theory: new results and applications. J. Approx. Theory 133(1), 38–99 (2005)
E. Lenglart, D. Lépingle, M. Pratelli, Présentation unifiée de certaines inégalités de la théorie des martingales. Séminaire de Probabilités, XIV, Lecture Notes in Math., vol. 784 (Springer, Berlin, 1980)
S. Meda, On the Littlewood-Paley-Stein g-function. Trans. Am. Math. Soc. 347(6), 2201–2212 (1995)
P.A. Meyer, Démonstration probabiliste de certaines inégalités de Littlewood-Paley. I. Les inégalités classiques. Séminaire de Probabilités, X, Lecture Notes in Math., vol. 511 (Springer, Berlin, 1976), pp. 125–141
P.-A. Meyer, Sur la théorie de Littlewood-Paley-Stein (d’après Coifman-Rochberg-Weiss et Cowling). Séminaire de probabilités, XIX, Lecture Notes in Math., vol. 1123 (Springer, Berlin, 1985), pp. 113–129
I. Shigekawa, The Meyer Inequality for the Ornstein-Uhlenbeck Operator in L 1 and Probabilistic Proof of Stein’s L p Multiplier Theorem. Trends in Probability and Related Analysis (Taipei, 1996) (World Scientific, River Edge, 1997), pp. 273–288
E.M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematics Studies, vol. 63 (Princeton University Press, Princeton, 1970)
Acknowledgements
The author is member of the GNAMPA group of the Istituto Nazionale di Alta Matematica (INdAM). He also thanks G.M. Dall’Ara for many discussions on the subject.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Trevisan, D. (2014). A Short Proof of Stein’s Universal Multiplier Theorem. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-11970-0_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11969-4
Online ISBN: 978-3-319-11970-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)