Martingale operators and Hardy spaces generated by them

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1. [1] N. Asmar and S. Montgomery-Smith, Littlewood-Paley theory on solenoids, Colloq. Math. 65 (1993), 69-82. 
2. [2] N. L. Bassily and J. Mogyoródi, On the $BM{O}_{\Phi }$-spaces with general Young function, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 27 (1984), 215-227. Zbl0581.60036
3. [3] C. Bennett and R. Sharpley, Interpolation of Operators, Pure and Appl. Math. 129, Academic Press, New York, 1988. Zbl0647.46057
4. [4] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. Zbl0344.46071
5. [5] A. Bernard et B. Maisonneuve, Décomposition atomique de martingales de la classe $H^1$, in: Séminaire de Probabilités XI, Lecture Notes in Math. 581, Springer, Berlin, 1977, 303-323. Zbl0384.60032
6. [6] O. Blasco, Interpolation between $H_B{0}^1$ and $L_B{1}^p$, Studia Math. 92 (1989), 205-210. 
7. [7] O. Blasco and Q. Xu, Interpolation between vector-valued Hardy spaces, J. Funct. Anal. 102 (1991), 331-359. Zbl0759.46066
8. [8] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. Zbl0301.60035
9. [9] D. L. Burkholder, B. J. Davis and R. F. Gundy, Integral inequalities for convex functions of operators on martingales, in: Proc. Sixth Berkeley Sympos. Math. Statist. and Probab., Univ. of California Press, 1972, 223-240. Zbl0253.60056
10. [10] D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249-304. Zbl0223.60021
11. [11] L. Chevalier, Démonstration atomique des inégalités de Burkholder-Davis-Gundy, Ann. Sci. Univ. Clermont-Ferrand 67 (1979), 19-24. Zbl0406.60039
12. [12] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
13. [13] B. J. Davis, On the integrability of the martingale square function, Israel J. Math. 8 (1970), 187-190. Zbl0211.21902
14. [14] C. Fefferman, N. M. Rivière and Y. Sagher, Interpolation between $H^p$ spaces: the real method, Trans. Amer. Math. Soc. 191 (1974), 75-81. Zbl0285.41006
15. [15] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-194. Zbl0257.46078
16. [16] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973. 
17. [17] R. Hanks, Interpolation by the real method between BMO, $L^{\alpha }(0<\alpha <\infty )$ and $H^{\alpha }$ (0< α< ∞), Indiana Univ. Math. J. 26 (1977), 679-689. 
18. [18] C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199-215. Zbl0321.60041
19. [19] C. Herz, $H_p$-spaces of martingales, 0<p ≤ 1, Z. Wahrsch. Verw. Gebiete 28 (1974), 189-205. Zbl0269.60040
20. [20] P. Hitczenko, Upper bounds for the $L_p$-norms of martingales, Probab. Theory Related Fields 86 (1990), 225-238. Zbl0677.60017
21. [21] S. Janson and P. Jones, Interpolation between $H^p$ spaces: the complex method, J. Funct. Anal. 48 (1982), 58-80. Zbl0507.46047
22. [22] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. Zbl0102.04302
23. [23] D. Lepingle, La variation d'ordre p des semi-martingales, Z. Wahrsch. Verw. Gebiete 36 (1976), 295-316. Zbl0325.60047
24. [24] D. Lepingle, Quelques inégalités concernant les martingales, Studia Math. 59 (1976), 63-83. Zbl0413.60046
25. [25] M. Milman, On interpolation of martingale $L^p$ spaces, Indiana Univ. Math. J. 30 (1981), 313-318. Zbl0501.46066
26. [26] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971. 
27. [27] G. Pisier and Q. Xu, The strong p-variation of martingales and orthogonal series, Probab. Theory Related Fields 77 (1988), 497-514. Zbl0632.60004
28. [28] M. Pratelli, Sur certains espaces de martingales localement de carré intégrable, in: Séminaire de Probabilités X, Lecture Notes in Math. 511, Springer, Berlin, 1976, 401-413. 
29. [29] N. M. Rivière and Y. Sagher, Interpolation between $L^{\infty }$ and $H^1,$ the real method, J. Funct. Anal. 14 (1973), 401-409. 
30. [30] H. P. Rosenthal, On the subspaces of $L^p(p>2)$ spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273-303. Zbl0213.19303
31. [31] F. Schipp, The dual space of martingale VMO space, in: Proc. Third Pannonian Sympos. Math. Statist., Visegrád, 1982, 305-315. 
32. [32] E. M. Stein, Topics in Harmonic Analysis, Princeton Univ. Press, 1970. Zbl0193.10502
33. [33] J.-O. Strömberg, Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J. 28 (1979), 511-544. Zbl0429.46016
34. [34] F. Weisz, Interpolation between martingale Hardy and BMO spaces, the real method, Bull. Sci. Math. 116 (1992), 145-158. Zbl0776.46018
35. [35] F. Weisz, Martingale Hardy spaces for 0<p ≤ 1, Probab. Theory Related Fields 84 (1990), 361-376. Zbl0687.60046
36. [36] F. Weisz, Martingale Hardy Spaces and Their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994. Zbl0796.60049
37. [37] T. H. Wolff, A note on interpolation spaces, in: Lecture Notes in Math. 908, Springer, Berlin, 1982, 199-204. 
38. [38] K. Yosida, Functional Analysis, Springer, Berlin, 1980. 

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