no. 21-22
Harmonic analysis/Functional analysis
Marcinkiewicz r-classes and Fourier series expansions of operator ergodic Stieltjes convolutions
[Mr(T), séries dʼopérateurs de Fourier et « Stieltjes convolutions »]

Présenté par : Gilles Pisier

Berkson, Earl1
1 Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA
Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 813-815.

Cette note étudie (dans la topologie forte des opérateurs) les développements en séries de Fourier pour les « convolutions de Stieltjes » des fonctions dans les r-classes de Marcinkiewicz par dE, où E est la décomposition spectrale dʼune bijection linéaire arbitraire T telle que T soit un opérateur préservant la disjonction dont le module linéaire est à moyennes bornées. Lʼanalyse harmonique vectorielle qui en résulte étend le transfert traditionnel de Calderón–Coifman–G. Weiss, sans supposer les puissances uniformément bornées traditionnellement requises pour le transfert.

We study the Fourier series expansions in the strong operator topology for operator-valued Stieltjes convolutions of Marcinkiewicz r-classes against spectral decompositions of modulus-mean-bounded operators. The vector-valued harmonic analysis resulting can be viewed as an extension of traditional Calderón–Coifman–G. Weiss transference without being constrained by the latterʼs requirement of power-boundedness.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.017
Berkson, Earl 1

1 Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA 
@article{CRMATH_2013__351_21-22_813_0,
     author = {Berkson, Earl},
     title = {Marcinkiewicz \protect\emph{r}-classes and {Fourier} series expansions of operator ergodic {Stieltjes} convolutions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {813--815},
     publisher = {Elsevier},
     volume = {351},
     number = {21-22},
     year = {2013},
     doi = {10.1016/j.crma.2013.10.017},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.10.017/}
}
TY  - JOUR
AU  - Berkson, Earl
TI  - Marcinkiewicz r-classes and Fourier series expansions of operator ergodic Stieltjes convolutions
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 813
EP  - 815
VL  - 351
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.10.017/
DO  - 10.1016/j.crma.2013.10.017
LA  - en
ID  - CRMATH_2013__351_21-22_813_0
ER  - 
%0 Journal Article
%A Berkson, Earl
%T Marcinkiewicz r-classes and Fourier series expansions of operator ergodic Stieltjes convolutions
%J Comptes Rendus. Mathématique
%D 2013
%P 813-815
%V 351
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.10.017/
%R 10.1016/j.crma.2013.10.017
%G en
%F CRMATH_2013__351_21-22_813_0
Berkson, Earl. Marcinkiewicz r-classes and Fourier series expansions of operator ergodic Stieltjes convolutions. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 813-815. doi : 10.1016/j.crma.2013.10.017. http://www.numdam.org/articles/10.1016/j.crma.2013.10.017/

[1] Berkson, E. Spectral theory and operator ergodic theory on super-reflexive Banach spaces, Stud. Math., Volume 200 (2010), pp. 221-246

[2] Berkson, E. Rotation methods in operator ergodic theory, N.Y. J. Math., Volume 17 (2011), pp. 21-39 http://nyjm.albany.edu/j/2011/17-2v.pdf (located online at)

[3] Berkson, E.; Gillespie, T.A. Mean-boundedness and Littlewood–Paley for separation-preserving operators, Trans. Amer. Math. Soc., Volume 349 (1997), pp. 1169-1189

[4] Berkson, E.; Gillespie, T.A. Shifts as models for spectral decomposability on Hilbert space, J. Oper. Theory, Volume 50 (2003), pp. 77-106

[5] Coifman, R.; Rubio de Francia, J.L.; Semmes, S. Multiplicateurs de Fourier de Lp(R) et estimations quadratiques, C. R. Acad. Sci. Paris, Ser. I, Volume 306 (1988), pp. 351-354

Cité par Sources :