ArticleOriginal scientific text
Title
An extension of an inequality due to Stein and Lepingle
Authors 1
Affiliations
- Department of Numerical Analysis, L. Eötvös University, Múzeum krt. 6-8, H-1088 Budapest, Hungary
Abstract
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.
Bibliography
- N. Asmar and S. Montgomery-Smith, Littlewood-Paley theory on solenoids, Colloq. Math. 65 (1993), 69-82.
- D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42.
- C. Dellacherie and P.-A. Meyer, Probabilities and Potential B, North-Holland Math. Stud. 72, North-Holland, 1982.
- A. M. Garsia, Martingale Inequalities, Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973.
- C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199-215.
- C. Herz,
- D. Lepingle, Quelques inégalités concernant les martingales, Studia Math. 59 (1976), 63-83.
- D. Lepingle, Une inégalite de martingales, in: Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, 134-137.
- E. M. Stein, Topics in Harmonic Analysis, Princeton Univ. Press, 1970.
- F. Weisz, Duality results and inequalities with respect to Hardy spaces containing function sequences, J. Theor. Probab. 9 (1996), 301-316.
- F. Weisz, Martingale Hardy Spaces and their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994.
- F. Weisz, Martingale operators and Hardy spaces generated by them, Studia Math. 114 (1995), 39-70.
Pages:
55-61
Main language of publication
English
Received
1995-09-26
Published
1996
Exact and natural sciences