A counterexample concerning the relation between decoupling constants and UMD-constants

Transactions of the American Mathematical Society

Volumn 351, Issue 4, 1999, Pages 1355-1375

  Geiss, Stefan ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Interpolation of danach spaces; Superreflexive banach spaces; Unconditional constants; Vector valued martingales

Indexed keywords

EID: 26244441837     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02093-0     Document Type: Article

References (23)

1. D.J. Aldous. Unconditional bases and martingales in LP(F). Math. Proc. Camb. Phil. Soc., 85:117-123, 1979. MR 80b:G0009
2. N.H. Asmar and S.J. Montgomery-Smith. On the distribution of Sidon series. Ark. Math., 31(1):13-2G, 1993. MR 94i:43006
3. B. Beauzamy. Introduction to Banach spaces and their geometry, volume 68 of Mathematics Studies. North-Holland, Amsterdam, New York, Oxford, 1985. MR 88f:46021
4. J. Bergh and J. Löfström. Interpolation spaces. An introduction. Springer, 1976. MR 58:2349
5. J. Bourgain. Some remarks on Banach spaces in which martingale difference sequences are unconditional. Ark. Mat., 21:163-168, 1983. MR 85a:46011
6. D.L. Burkholder. Martingales and Fourier analysis in Banach spaces. In C.I.M.E. Lectures, Varenna (Como), Italy, 1985, volume 1206 of Lect. Notes in Math., pages 61-108. Springer, 1986. MR 88c:42017
7. D.L. Burkholder. Explorations in martingale theory and its applications. In Ecole d'Eté de Probabilités de Saint-Flour XIX-1989, volume 1464 of Lect. Notes Math., pages 1-66. Springer, 1991. MR 92m:60037
8. D.L. Burkholder, B.J. Davis, and R.F. Gundy. Integral inequalities for convex functions of operators on martingales. In Proc. 6th Berkeley Sympos, volume 2 of Math. Statist. Probab., pages 223-240, 1972. MR 53:4214
9. D.L. Burkholder and R.F. Gundy. Extrapolation and interpolation of quasilinear operators on martingales. Acta Math., 124:249-304, 1970. MR 55:13567
10. D.H.J. Garling. Random martingale transform inequalities. In Probability in Banach spaces 6. Proceedings of the sixth international conference, Sandbjerg, Denmark 1986, pages 101-119. Birkhäuser, 1990. MR 92a:60111
11. A.M. Garsia. Martingale inequalities. Seminar Notes on Recent Progress. Benjamin, Reading, 1973. MR 56:6844
12. S. Geiss. BMO,-spaces and applications to extrapolation theory. Studio, Math., 122(3):235274, 1997. MR 98a:46037
13. P. Hitczenko. Upper bounds for the Lp-norms of martingales. Probab. Th. Rel. Fields, 86:225238, 1990. MR 92a:60112
14. P. Hitczenko. Domination inequality for martingale transforms of a Rademacher sequence. Israel J. Math., 84:161-178, 1993. MR 941:60061
15. R.C. James. Some self dual properties of normed linear spaces. Ann. of Math. Studies, 69:159175, 1972. MR 56:12849
16. R.C. James. Super-reflexive Banach spaces. Can. J. Math., 5:896-904, 1972. MR 47:9248
17. M. Ledoux and M. Talagrand. Probability in Banach spaces. Springer, 1991. MR 93c:60001
18. J. Lindenstrauss and L. Tzafriri. Classical Banach spaces I/II. Springer, 1977/1979. MR 58:17766 MR 81c:46001
19. B. Maurey. Systeme de Haar. Seminaire Maurey-Schwartz, Ecole Polytechnique, Paris, 19741975. MR 54:8851
20. G. Pisier. Un exemple concernant la superréflexivité. Séminaire Maurey-Schwartz, Ecole Polytechnique, Paris, 1974-1975. MR 53:14090
21. G. Pisier. Martingales with values in uniformly convex spaces. Israel J. Math., 20:326-350, 1975. MR 52:14940
22. G. Pisier and Q. Xu. Random series in the real interpolation spaces between the spaces vp. In Israel Functional Seminar, GAFA, volume 1267 of Lect. Notes Math., pages 185-209. Springer, 1987. MR 89d:46011
23. J. Wenzel. Personal communication.