This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Benedek, R. Panzone: The spaces L p with mixed norm. Duke Math. J. 28 (1961), 301–324.
S. Bochner: Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind. Fundamenta Math. 20 (1933), 262–276.
J. Bourgain: Some remarks on Banach spaces in which martingale differences are unconditional. Arkiv Mat. 21 (1983), 163–168.
J. Bourgain: Extension of a result of Benedek, Calderon and Panzone. Arkiv Mat. 22 (1984), 91–95.
J. Bourgain: Vector valued singular integrals and the H 1-BMO duality. Preprint.
D. L. Burkholder: Martingale Transforms. Ann. Math. Statist. 37 (1966), 1494–1504.
D. L. Burkholder: A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Ann. Probability 9 (1981), 997–1011.
D. L. Burkholder, R. F. Gundy: Extrapolation and interpolation of quasilinear operators on martingales. Acta. Math. 124 (1970), 249–304.
F. Cobos: Some spaces in which martingale differences are unconditional. Preprint.
R. Coifman, C. Fefferman: Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241–250.
C. Fefferman, E. M. Stein: Some maximal inequalities. Amer. J. Math. 93 (1971), 107–115.
J. Garcia-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. North Holland, Amsterdam, 1985.
D. J. H. Garling: Brownian motion and UMD spaces. These Proceedings.
R. F. Gundy, R. L. Wheeden: Weighted integral inequalities for the nontangential maximal function, Lusin area integral and Walsh-Paley series. Studia Math. 49 (1974), 107–124.
R. C. James: Super-reflexive Banach spaces. Can. J. Math. 24 (1972), 896–904.
S. Kwapien: Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients. Studia Math. 44 (1972), 583–595.
J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces II. Function Spaces. Springer-Verlag, Berlin, 1979.
B. Maurey: Théorèmes de Factorization pour les Opérateurs Linéaires à Valeurs dans les Espaces L p. Asterique No. 11. Soc. Math. France, 1974.
B. Maurey: Systeme de Haar. Sem. Maurey-Schwartz, 1974–75, Ecole Polytechnique, Paris.
G. Pisier: Sur les espaces de Banach qui ne contiennent pas uniformement de ℓ 1n . C. R. Acad. Sci. Paris, Ser. A, 277 (1983), 991–994.
G. Pisier: Martingales with values in uniformly convex spaces. Israel J. Math. 20 (1975), 326–350.
G. Pisier: Un exemple concernant la super-reflexivite. Sem. Maurey-Schwartz, 1974, Ecole Polytechnique, Paris.
G. Pisier: Some applications of the complex interpolation method to Banach lattices. Journal d'Anal. Math. 35 (1979), 264–281.
J. L. Rubio de Francia: Fourier series and Hilbert transforms with values in UMD Banach spaces. Studia Math. 81 (1985).
J. L. Rubio de Francia: Linear operators in Banach lattices and weighted L 2 inequalities. Math. Nachr. (1986), to appear.
J. L. Rubio de Francia, J. L. Torea: Some Banach techniques in vector valued Fourier Analysis. Colloquium Math., to appear.
J. L. Torrea: Análisis de Fourier de funciones vectoriales. Tesis, Univ. Zaragoza, 1980.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Rubio de Francia, J.L. (1986). Martingale and integral transforms of banach space valued functions. In: Bastero, J., San Miguel, M. (eds) Probability and Banach Spaces. Lecture Notes in Mathematics, vol 1221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099115
Download citation
DOI: https://doi.org/10.1007/BFb0099115
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17186-7
Online ISBN: 978-3-540-47344-2
eBook Packages: Springer Book Archive