Operator-valued martingale transforms

Tohoku Mathematical Journal

Volumn 52, Issue 3, 2000, Pages 449-474

  Martínez, Teresa ^a   Torrea, José L ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034343781     PISSN: 00408735     EISSN: None     Source Type: Journal    
DOI: 10.2748/tmj/1178207823     Document Type: Article

References (24)

1. D. G. Austin, A sample function property for martingales, Ann. Math. Statist. 37 (1966), 1396-1397.
2. R. Banuelos, Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), 547-563.
3. n, J. Funct. Anal. 145 (1997), 224-265.
4. R. Bañuelos and Gang Wang, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J. 80 (1995), 575-600.
5. R. Bañuelos and Gang Wang, Orthogonal martingales under differential subordination and applications to Riesz transforms, Illinois J. Math. 40 (1996), 678-691.
6. A. Benedek, A. R Calderón and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. USA 48 (1962), 356-365.
7. J. Bourgain, Extension of a result of Benedeck, Calderon and Panzone, Ark. Mat. 22 (1984), 91-95.
8. D. L. Burkholder, Martingale Transforms, Ann. Math. Stat. 37 (1966), 1494-1504.
9. D. L. Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), 997-1011.
10. D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasilinear operators on martingales, Acta Math. 124 (1970), 249-304.
11. D. L. Burkholder, R. F. Gundy and M. Silverstein, A maximal function characterization of the class HP, Trans. Amer. Math. Soc. 157 (1971), 137-153.
12. A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139.
13. S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand. 22(1968), 21-41.
14. D. J. Davis, On the integrability of the martingale square function, Israel J. Math. 8 (1970), 187-190.
15. J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys, No. 15, Amer. Math. Soc., Providence, R.I., 1977.
16. J. L. Doob, Stochastic Processes, John Wiley, New York, 1953.
17. C. Fefferman and E. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
18. J. García-Cuerva, R. Macías and J. L. Torrea, The Hardy-Littlewood property of Banach lattices, Israel J. Math. 83 (1993), 177-201.
19. 1 -bounded martingales, Ann. Math. Statist. 39 (1968), 134-138.
20. S. Kwapien, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972), 583-595.
21. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II. Function spaces, Ergeh. Math. Grenzgeb. 97, Springer-Verlag, Berlin, 1979.
22. B. Maure Y, Système de Haar, Séminaire Maurey-Schwartz 1974-75, Centre Math., École Polytech., Paris, 1975.
23. J. L. Rubio de Francia, Martingale and integral transforms of Banach space valued functions, in Conference on Probability and Banach spaces (Zaragoza, 1985), 195-222, Lecture Notes in Math. 1221, SpringerVerlag, Berlin-New York, 1986.
24. F. Weisz, Martingale Hardy spaces and their applications in Fourier Analysis, Lecture Notes in Math. 1568, Springer-Verlag, Berlin, 1994.