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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 champ

Nature: Original

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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 (

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 champ

Nature: Original

Retrieve article from Numdam