We give new results on square functions
Nous obtenons de nouveaux résultats sur les fonctions carrées
Keywords: sectorial operators, $H^{\infty }$ functional calculus, square functions, $R$-boundedness, admissibility
Mot clés : opérateurs sectoriels, calcul fonctionnel $H^{\infty }$, fonctions carrées, $R$-bornitude, admissibilité
@article{BSMF_2004__132_1_137_0, author = {Le Merdy, Christian}, title = {On square functions associated to sectorial operators}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {137--156}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {132}, number = {1}, year = {2004}, doi = {10.24033/bsmf.2462}, zbl = {1066.47013}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/bsmf.2462/} }
TY - JOUR AU - Le Merdy, Christian TI - On square functions associated to sectorial operators JO - Bulletin de la Société Mathématique de France PY - 2004 SP - 137 EP - 156 VL - 132 IS - 1 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2462/ DO - 10.24033/bsmf.2462 LA - en ID - BSMF_2004__132_1_137_0 ER -
%0 Journal Article %A Le Merdy, Christian %T On square functions associated to sectorial operators %J Bulletin de la Société Mathématique de France %D 2004 %P 137-156 %V 132 %N 1 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/bsmf.2462/ %R 10.24033/bsmf.2462 %G en %F BSMF_2004__132_1_137_0
Le Merdy, Christian. On square functions associated to sectorial operators. Bulletin de la Société Mathématique de France, Volume 132 (2004) no. 1, pp. 137-156. doi : 10.24033/bsmf.2462. http://archive.numdam.org/articles/10.24033/bsmf.2462/
[1] « The operator valued Marcinkiewicz multiplier theorem and maximal regularity », Math. Z. 240 (2002), p. 311-343. | MR | Zbl
& -[2] P. Auscher, X. Duong & A. McIntosh - in preparation.
[3] « Holomorphic functional calculi of operators, quadratic estimates and interpolation », Indiana Univ. Math. J. 46 (1997), p. 375-403. | MR | Zbl
, & -[4] « Schauder decompositions and multiplier theorems », Studia Math. 138 (2000), p. 135-163. | MR | Zbl
, , & -[5] « An operator valued transference principle and maximal regularity on vector valued -spaces », Proc. of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Sciences (Bad Herrenalb, 1998) (G. Lumer & L. Weis, éds.), Marcel Dekker, New-York, 2001, p. 67-87. | MR | Zbl
& -[6] « Banach space operators with a bounded functional calculus », J. Austr. Math. Soc. 60 (1996), p. 51-89. | MR | Zbl
, , & -[7] Bounded analytic functions, Pure and applied Mathematics, vol. 96, Academic Press, 1981. | MR | Zbl
-[8] « Admissible observation operators. Semigroup criteria of admissibility », Int. Equ. Oper. Theory 25 (1996), p. 182-198. | MR | Zbl
& -[9] « The Weiss conjecture on admissibility of observation operators for contraction semigroups », Int. Equ. Oper. Theory 40 (2001), p. 231-243. | MR | Zbl
& -[10] « Admissible and weakly admissible observation operators for the right shift semigroup », Proc. Edinburgh Math. Soc. 45 (2002), p. 353-362. | MR | Zbl
, & -[11] « Weak admissibility does not imply admissibility for analytic semigroups », 2003. | MR | Zbl
, & -[12] « Disproof of two conjectures of George Weiss », Preprint, 2000.
& -[13] « A solution to the problem of -maximal regularity », Math. Z. 235 (2000), p. 559-568. | MR | Zbl
& -[14] « The calculus and sums of closed operators », Math. Ann. 321 (2001), p. 319-345. | MR | Zbl
& -[15] « A joint functional calculus for sectorial operators with commuting resolvents », Proc. London Math. Soc. 77 (1998), p. 387-414. | MR | Zbl
, & -[16] « The Weiss conjecture for bounded analytic semigroups », J. London Math. Soc. (2) 67 (2003), p. 715-738. | MR | Zbl
-[17] Classical Banach spaces II, Springer Verlag, Berlin, 1979. | MR | Zbl
& -[18] « Operators which have an functional calculus », Miniconference on operator theory and partial differential equations, Proc. of CMA, Canberra, vol. 14, 1986, p. 210-231. | MR | Zbl
-[19] « Operators of type without a bounded functional calculus », Miniconference on operators in analysis, Proc. of CMA, Canberra, vol. 24, 1989, p. 159-172. | MR | Zbl
& -[20] « Admissible observation operators for the right shift semigroup », Math. Cont. Signals Systems 13 (2000), p. 179-192. | MR | Zbl
& -[21] « A new approach to maximal -regularity », Proc. of the Sixth International Conference on Evolution Equations and their Applications in Physical and Life Sciences (Bad Herrenalb, 1998) (G. Lumer & L. Weis, éds.), Lecture Notes in Pure and Appl. Math., vol. 215, Marcel Dekker, New-York, 2001, p. 195-214. | MR | Zbl
-[22] -, « Operator valued Fourier multiplier theorems and maximal regularity », Math. Ann. 319 (2001), p. 735-758. | MR | Zbl
[23] « Admissibility of unbounded control operators », SIAM J. Control Optim. 27 (1989), p. 527-545. | MR | Zbl
-[24] -, « Admissible observation operators for linear semigroups », Israel J. Math. 65 (1989), p. 17-43. | MR
[25] -, « Two conjectures on the admissibility of control operators », Estimation and control of distributed parameter systems, Birkäuser Verlag, 1991, p. 367-378. | MR | Zbl
Cited by Sources: