Hardy spaces consisting of adapted function sequences and generated by the q-variation and by the conditional q-variation are considered. Their dual spaces are characterized and an inequality due to Stein and Lepingle is extended.
@article{bwmeta1.element.bwnjournal-article-cmv71i1p55bwm, author = {Weisz, Ferenc}, title = {An extension of an inequality due to Stein and Lepingle}, journal = {Colloquium Mathematicae}, volume = {70}, year = {1996}, pages = {55-61}, zbl = {0859.60041}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p55bwm} }
Weisz, Ferenc. An extension of an inequality due to Stein and Lepingle. Colloquium Mathematicae, Tome 70 (1996) pp. 55-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p55bwm/
[000] [1] N. Asmar and S. Montgomery-Smith, Littlewood-Paley theory on solenoids, Colloq. Math. 65 (1993), 69-82.
[001] [2] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. | Zbl 0301.60035
[002] [3] C. Dellacherie and P.-A. Meyer, Probabilities and Potential B, North-Holland Math. Stud. 72, North-Holland, 1982.
[003] [4] A. M. Garsia, Martingale Inequalities, Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973.
[004] [5] C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199-215. | Zbl 0321.60041
[005] [6] C. Herz, -spaces of martingales, 0 < p ≤ 1, Z. Wahrsch. Verw. Gebiete 28 (1974), 189-205. | Zbl 0269.60040
[006] [7] D. Lepingle, Quelques inégalités concernant les martingales, Studia Math. 59 (1976), 63-83. | Zbl 0413.60046
[007] [8] D. Lepingle, Une inégalite de martingales, in: Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, 134-137.
[008] [9] E. M. Stein, Topics in Harmonic Analysis, Princeton Univ. Press, 1970. | Zbl 0193.10502
[009] [10] F. Weisz, Duality results and inequalities with respect to Hardy spaces containing function sequences, J. Theor. Probab. 9 (1996), 301-316. | Zbl 0876.60024
[010] [11] F. Weisz, Martingale Hardy Spaces and their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994. | Zbl 0796.60049
[011] [12] F. Weisz, Martingale operators and Hardy spaces generated by them, Studia Math. 114 (1995), 39-70. | Zbl 0822.60043