An extension of an inequality due to Stein and Lepingle

Ferenc Weisz

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 1, page 55-61
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

Weisz, Ferenc. "An extension of an inequality due to Stein and Lepingle." Colloquium Mathematicae 71.1 (1996): 55-61. <http://eudml.org/doc/210427>.

@article{Weisz1996,
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.},
author = {Weisz, Ferenc},
journal = {Colloquium Mathematicae},
keywords = {BMO spaces; Hardy spaces; conditional -variation; predictable prediction},
language = {eng},
number = {1},
pages = {55-61},
title = {An extension of an inequality due to Stein and Lepingle},
url = {http://eudml.org/doc/210427},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Weisz, Ferenc
TI - An extension of an inequality due to Stein and Lepingle
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 1
SP - 55
EP - 61
AB - 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.
LA - eng
KW - BMO spaces; Hardy spaces; conditional -variation; predictable prediction
UR - http://eudml.org/doc/210427
ER -

References

top
  1. [1] N. Asmar and S. Montgomery-Smith, Littlewood-Paley theory on solenoids, Colloq. Math. 65 (1993), 69-82. 
  2. [2] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. Zbl0301.60035
  3. [3] C. Dellacherie and P.-A. Meyer, Probabilities and Potential B, North-Holland Math. Stud. 72, North-Holland, 1982. 
  4. [4] A. M. Garsia, Martingale Inequalities, Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973. 
  5. [5] C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199-215. Zbl0321.60041
  6. [6] C. Herz, H p -spaces of martingales, 0 < p ≤ 1, Z. Wahrsch. Verw. Gebiete 28 (1974), 189-205. Zbl0269.60040
  7. [7] D. Lepingle, Quelques inégalités concernant les martingales, Studia Math. 59 (1976), 63-83. Zbl0413.60046
  8. [8] D. Lepingle, Une inégalite de martingales, in: Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, 134-137. 
  9. [9] E. M. Stein, Topics in Harmonic Analysis, Princeton Univ. Press, 1970. Zbl0193.10502
  10. [10] F. Weisz, Duality results and inequalities with respect to Hardy spaces containing function sequences, J. Theor. Probab. 9 (1996), 301-316. Zbl0876.60024
  11. [11] F. Weisz, Martingale Hardy Spaces and their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994. Zbl0796.60049
  12. [12] F. Weisz, Martingale operators and Hardy spaces generated by them, Studia Math. 114 (1995), 39-70. Zbl0822.60043

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.