XV: 10, 151-166, LNM 850 (1981)
MEYER, Paul-André
Retour sur la théorie de Littlewood-Paley (
Applications of martingale theory,
Markov processes)
The word ``original'' may be considered misleading, since this paper is essentially a re-issue of
1010 (see the corresponding review), with a slightly better pedagogy, and the correction of a mistake. Meanwhile, Varopoulos had independently rediscovered the subject (
J. Funct. Anal., 38, 1980)
Comment: See an application to the Ornstein-Uhlenbeck semigroup
1816, see
1818 for a related topic, and the report
1908 on Cowling's extension of Stein's work. Bouleau-Lamberton
2013 replace the auxiliary Brownian motion by a stable process to obtain further inequalities. In another direction, the subject is developed in the theory of $\Gamma_2$ due to Bakry
1910, see also Bakry-Émery
1912; a general account of this point of view in semigroup theory is given by Bakry in his 1992 Saint-Flour lectures (LN 1581)
Keywords: Littlewood-Paley theory,
Semigroup theory,
Riesz transforms,
Brownian motion,
Inequalities,
Harmonic functions,
Singular integrals,
Carré du champNature: Original
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