Theory of $\mathcal{H}_p$-spaces for continuous filtrations in von Neumann algebras

Theory of

ℋ_{p}

-spaces for continuous filtrations in von Neumann algebras

Junge, Marius ; Perrin, Mathilde

Astérisque, no. 362 (2014) , 140 p.

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MR 3241706 | Zbl 1331.46002

BibTeX
RIS

@book{AST_2014__362__R1_0,
     author = {Junge, Marius and Perrin, Mathilde},
     title = {Theory of <span class="mathjax-formula">$\mathcal{H}_p$</span>-spaces for continuous filtrations in von {Neumann} algebras},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {362},
     year = {2014},
     zbl = {1331.46002},
     mrnumber = {3241706},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2014__362__R1_0/}
}

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AU  - Junge, Marius
AU  - Perrin, Mathilde
TI  - Theory of <span class="mathjax-formula">$\mathcal{H}_p$</span>-spaces for continuous filtrations in von Neumann algebras
T3  - Astérisque
PY  - 2014
DA  - 2014///
IS  - 362
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2014__362__R1_0/
UR  - https://zbmath.org/?q=an%3A1331.46002
UR  - https://www.ams.org/mathscinet-getitem?mr=3241706
LA  - en
ID  - AST_2014__362__R1_0
ER  -

Junge, Marius; Perrin, Mathilde. Theory of $\mathcal{H}_p$-spaces for continuous filtrations in von Neumann algebras. Astérisque, no. 362 (2014), 140 p. http://numdam.org/item/AST_2014__362__R1_0/

Bibliographie
Cité par

[2] Bekjan (T.), Chen (Z.), Perrin (M.) & Yin (Z.) - Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales, Funct. Anal., t. 258 (2010), pp. 2483-2505. | Article | MR 2584751 | Zbl 1198.46047

[3] Bergh (J.) & Löfström (J.) - Interpolation Spaces. An introduction, Springer, New York, 1976. | MR 482275 | Zbl 0344.46071

[4] Burkholder (D. L.) - Martingale transforms, Ann. Math. Statist., t. 37 (1966), pp. 1494-1504. | Article | MR 208647 | Zbl 0306.60030

[5] Burkholder (D. L.), Distribution function inequalities for martingales, Ann. Probab., t. 1 (1973), pp. 19-42. | Article | MR 365692 | Zbl 0301.60035

[6] Burkholder (D. L.) & Gundy (R. F.) - Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math., t. 124 (1970), pp. 249-304. | Article | MR 440695 | Zbl 0223.60021

[7] Coifman (R. A.) - A real variable characterization of $H_{p}$ , Studia Math., t. 51 (1974), pp. 269-274. | Article | EuDML 217919 | MR 358318 | Zbl 0289.46037

[8] Davis (B.) - On the integrability of the martingale square function, Israel J. Math., t. 8 (1970), pp. 187-190. | Article | MR 268966 | Zbl 0211.21902

[9] Dellacherie (C.) & Meyer (P. A.) - Probabilités et potentiel, chapitres V à VIII. Théorie des martingales, Hermann, Paris, 1980. | MR 566768 | Zbl 0464.60001

[10] Fack (T.) & Kosaki (H.) - Generalized $s$ -numbers of $τ$ -measurable operators, Pacific J. Math., t. 123 (1986), pp. 269-300. | Article | MR 840845 | Zbl 0617.46063

[11] Garsia (A. M.) - Martingale inequalities: Seminar notes on recent progress, Math. Lecture Notes Series, W.A. Benjamin, Inc., Reading, Mass., London-Amsterdam, 1973. | MR 448538 | Zbl 0284.60046

[12] Groh (U.) - Uniform ergodic theorems for identity preserving Schwartz maps on $W^{*}$ -algebras, J. Operator Theory, t. 11 (1984), pp. 395-404. | MR 749170 | Zbl 0551.46046

[13] Gundy (R. F.) - A decomposition for $L^{1}$ -bounded martingales, Ann. Math. Statist., t. 39 (1968), pp. 134-138. | Article | MR 221573 | Zbl 0185.45102

[14] Haagerup (U.) - $L^{p}$ -spaces associated with an arbitrary von Neumann algebra, Algèbres d'opérateurs et leurs applications en physique mathématique (1979), pp.175-184. | MR 560633 | Zbl 0426.46045

[15] Haagerup (U.), Rosenthal (H.) & Sukochev (F. A.) - Banach embedding properties of noncommutative $L^{p}$ -spaces, vol. 163, Amer. Math. Soc., 2003. | MR 1963854 | Zbl 1045.46039

[16] Heinrich (S.) - Ultraproducts in Banach spaces theory, J. reine angew. Math., t. 313 (1980), pp. 72-104. | EuDML 152195 | MR 552464 | Zbl 0412.46017

[17] Henson (C. W.) & L. C. Moore (Jr) - The nonstandard theory of topological vector spaces, Trans. Amer. Math. Soc., t. 172 (1972), pp. 405-435. | Article | MR 308722 | Zbl 0254.46001

[18] Herz (C.) - Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc., t. 193 (1974), pp. 199-215. | Article | MR 353447 | Zbl 0321.60041

[19] Herz (C.), $H_{p}$ -spaces of martingales, $0 < p \leq 1, Z$ . Wahrscheinlichkeitstheorie und Verw. Gebiete, t. 28 (1974), pp. 189-205. | Zbl 0269.60040

[20] Janson (S.) & Jones (P.) - Interpolation between $H_{p}$ -spaces, the complex method, J. Funct. Anal., t. 48 (1982), pp. 58-80. | Article | MR 671315 | Zbl 0507.46047

[21] Junge (M.) - Doob's inequality for non-commutative martingales, J. reine angew. Math., t. 549 (2002), pp. 149-190. | MR 1916654 | Zbl 1004.46043

[22] Junge (M.) & Mei (T.) - Noncommutative Riesz transforms - A probabilistic approach, Amer. J. Math., t. 132 (2010), pp. 611-680. | Article | MR 2666903 | Zbl 1200.46056

[23] Junge (M.) & Musat (M.) - A noncommutative version of the John-Nirenberg theorem, Trans. Amer. Math. Soc., t. 59 (2007), pp. 115-142. | Article | MR 2247885 | Zbl 1173.46046

[24] Junge (M.) & Parcet (J.) - Mixed-norm inequalities and operator space $L_{p}$ embedding theory, Mem. Amer. Math. Soc., vol. 203, Amer. Math. Soc., 2010. | MR 2589944 | Zbl 1220.46041

[25] Junge (M.), Parcet (J.) & Xu (Q.) - Rosenthal type inequalities for free chaos, Ann. Probab., t. 35 (2007), pp. 1374-1437. | Article | MR 2330976 | Zbl 1125.46054

[26] Junge (M.) & Sherman (D.) - Noncommutative $L_{p}$ modules, J. Operator Theory, t. 53 (2005), pp. 3-34. | MR 2132686 | Zbl 1078.46046

[27] Junge (M.) & Xu (Q.) - Noncommutative Burkholder-Rosenthal inequalities, Ann. Probab., t. 31 (2003), pp. 948-995. | Article | MR 1964955 | Zbl 1041.46050

[28] Junge (M.) & Xu (Q.), On the best constants in some non-commutative martingale inequalities, Bull. London Math. Soc., t. 37 (2005), pp. 243-253. | Article | MR 2119024 | Zbl 1088.46037

[29] Junge (M.) & Xu (Q.), Noncommutative maximal ergodic theorems, J. Amer. Math. Soc., t. 20 (2007), pp. 385-439. | Article | MR 2276775 | Zbl 1116.46053

[30] Junge (M.) & Xu (Q.), Noncommutative Burkholder-Rosenthal inequalities II. Applications, Israel J. Math., t. 167 (2008), pp. 227-282. | Article | MR 2448025 | Zbl 1217.46043

[31] Kadison (R. V.) & Ringrose (J. R.) - Fundamentals of the theory of operator algebras. Vol. I, Graduate Studies in Math., vol. 15, American Mathematical Society, Providence, RI, 1997 (Elementary theory, reprint of the 1983 original). | MR 1468229 | Zbl 0888.46039

[32] Lust-Piquard (F.) - Inégalités de Khintchine dans $C_{p} (1 < p < \infty)$ , C. R. Acad. Sci. Paris, t. 303 (1986), pp. 289-292. | MR 859804 | Zbl 0592.47038

[33] Lust-Piquard (F.) & Pisier (G.) - Non commutative Khintchine and Paley inequalities, Ark. Math., t. 29 (1991), pp. 241-260. | Article | MR 1150376 | Zbl 0755.47029

[34] Musat (M.) - Interpolation between noncommutative BMO and noncommutative $L_{p}$ -spaces, J. Funct. Anal., t. 202 (2003), pp. 195-225. | Article | MR 1994770 | Zbl 1042.46038

[35] Parcet (J.) - Weak type estimates associated to Burkholder's martingale inequality, Rev. Mat. Iberoam., t. 23 (2007), pp. 1011-1037. | Article | EuDML 43624 | MR 2414501 | Zbl 1155.46033

[36] Parcet (J.) & Randrianantoanina (M.) - Gundy's decomposition for non-commutative martingales and applications, Proc. London Math. Soc. (3), t. 93 (2006), pp. 227-252. | Article | MR 2235948 | Zbl 1119.46049

[37] Perrin (M.) - A noncommutative Davis' decomposition for martingales, J. Lond. Math. Soc., t. 80 (2009), pp. 627-648. | Article | MR 2559120 | Zbl 1225.46048

[38] Pisier (G.) - Non-commutative vector valued $L_{p}$ -spaces and completely $p$ -summing maps, Astérisque, t. 247 (1998). | Numdam | MR 1648908 | Zbl 0937.46056

[39] Pisier (G.), An inequality for $p$ -orthogonal sums in non-commutative $L_{p}$ , Illinois J. Math., t. 44 (2000), pp. 901-923. | MR 1804311 | Zbl 0976.60016

[40] Pisier (G.) & Xu (Q.) - Non-commutative martingale inequalities, Comm. Math. Phys., t. 189 (1997), pp. 667-698. | Article | Zbl 0898.46056

[41] Pisier (G.), Non-commutative $L^{p}$ -spaces, Handbook of the geometry of Banach spaces, vol. 2, North-Holland, Amsterdam, 2003. | Article | Zbl 1046.46048

[42] Pratelli (M.) - Sur certains espaces de martingales localement de carré intégrable, Séminaire de Probabilités, X (seconde partie : théorie des intégrales stochastiques), 1974/1975, Univ. Strasbourg, Springer, Berlin, 1976. | EuDML 113085 | Numdam | Zbl 0339.60043

[43] Randrianantoanina (N.) - Kadec-Pelczynski decomposition for Haagerup $L^{p}$ -spaces, Math. Camb. Philos. Soc., t. 132 (2002), pp. 137-154. | Zbl 1037.46055

[44] Randrianantoanina (N.), Non-commutative martingale transforms, J. Funct. Anal., t. 194 (2002), pp. 181-212. | Zbl 1030.46083

[45] Randrianantoanina (N.), A weak type inequality for non-commutative martingales and applications, Proc. London Math. Soc. (3), t. 91 (2005), pp. 509-542. | Article | Zbl 1091.46040

[46] Randrianantoanina (N.), Conditioned square functions for noncommutative martingales, Ann. Probab., t. 35 (2007), pp. 1039-1070. | Article | Zbl 1155.46034

[47] Randrianantoanina (N.) & Xu (Q.) - Atomic and Davis decompositions for noncommutative martingales, Preprint.

[48] Raynaud (Y.) - On ultrapowers of noncommutative $L_{p}$ spaces, J. Operator Theory, t. 48 (2002), pp. 41-68. | Zbl 1029.46102

[49] Raynaud (Y.) & Xu (Q.) - On suspaces of non-commutative $L_{p}$ -spaces, J. Funct. Anal., t. 203 (2003), pp. 149-196. | Article | Zbl 1056.46056

[50] Ricard (E.) & Xu (Q.) - Khintchine type inequalities for reducer free products and applications, J. reine angew. Math., t. 599 (2006), pp. 27-59. | Zbl 1170.46052

[51] Sakai (S.) - $C^{*}$ -algebras and $W^{*}$ -algebras, Springer-Verlag, 1971. | Zbl 1024.46001

[52] Sims (B.) - Ultra-techniques in Banach space theory, Queen's Papers in Pure and Appl. Math., t. 60 (1982). | Zbl 0611.46019

[53] Sukochev (F.) & Xu (Q.) - Embedding of non-commutative $L^{p}$ -spaces, $p < 1$ , Arch. Math., t. 80 (2003), pp. 151-164. | Article | Zbl 1030.46081

[54] Takesaki (M.) - Theory of operator algebras. I, Springer-Verlag, New York, 1979. | Article

[55] Tam (P. K.) - Isometries of $l_{p}$ -spaces associated with semifinite von Neumann algebras, Trans. Amer. Math. Soc., t. 254 (1979), pp. 339-354. | Zbl 0408.46051

[56] Terp (M.) - $L_{p}$ -spaces associated with von Neumann Algebras, Notes, Copenhagen University, 1981.

[57] Voiculescu (D.) - Symmetries of some reduced free product $C^{*}$ -algebras, Lecture Notes in Math., vol. 1132, 1985. | Zbl 0618.46048

[58] Weisz (F.) - Martingale Hardy spaces for $0 < p \leq 1$ , Probab. Theory Related Fields, t. 84 (1990), pp. 361-376. | Article | Zbl 0687.60046

[59] Weisz (F.), Martingale Hardy Spaces and their Applications in Fourier Analysis, Lecture Notes in Math., vol. 1568, Springer-Verlag, Berlin, 1994. | Zbl 0796.60049

[60] Wolff (T.) - A note on interpolation space, Lecture Notes in Math., vol. 908, Springer-Verlag, Berlin, 1982. | Zbl 0517.46054

[61] Xu (Q.) - Some results related to interpolation on Hardy spaces of regular martingales, Israel J. Math., t. 91 (1995), pp. 173-187. | Article | Zbl 0833.46024

[62] Xu (Q.), Noncommutative $L_{p}$ -spaces and martingale inequalities, Book manuscript, 2007.