An application of two-parameter martingales in harmonic analysis

Ferenc Weisz

Studia Mathematica (1993)

  • Volume: 107, Issue: 2, page 115-126
  • ISSN: 0039-3223

Abstract

top
Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.

How to cite

top

Weisz, Ferenc. "An application of two-parameter martingales in harmonic analysis." Studia Mathematica 107.2 (1993): 115-126. <http://eudml.org/doc/216024>.

@article{Weisz1993,
abstract = {Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.},
author = {Weisz, Ferenc},
journal = {Studia Mathematica},
keywords = {duality results; two-parameter Vilenkin martingales; Fourier backwards martingales},
language = {eng},
number = {2},
pages = {115-126},
title = {An application of two-parameter martingales in harmonic analysis},
url = {http://eudml.org/doc/216024},
volume = {107},
year = {1993},
}

TY - JOUR
AU - Weisz, Ferenc
TI - An application of two-parameter martingales in harmonic analysis
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 2
SP - 115
EP - 126
AB - Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.
LA - eng
KW - duality results; two-parameter Vilenkin martingales; Fourier backwards martingales
UR - http://eudml.org/doc/216024
ER -

References

top
  1. [1] A. Benedek and R. Panzone, The spaces L P , with mixed norm, Duke Math. J. 28 (1961), 301-324. Zbl0107.08902
  2. [2] A. Bernard, Espaces H¹ de martingales à deux indices. Dualité avec les martingales de type <<BMO>>, Bull. Sci. Math. 103 (1979), 297-303. Zbl0403.60047
  3. [3] J. Brossard, Comparaison des “normes” L p du processus croissant et de la variable maximale pour les martingales régulières à deux indices. Théorème local correspondant, Ann. Probab. 8 (1980), 1183-1188. Zbl0454.60047
  4. [4] J. Brossard, Régularité des martingales à deux indices et inégalités de normes, in: Processus Aléatoires à Deux Indices, Lecture Notes in Math. 863, Springer, Berlin, 1981, 91-121. Zbl0473.60045
  5. [5] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. Zbl0301.60035
  6. [6] R. Cairoli, Une inégalité pour martingales à indices multiples et ses applications, in: Séminaire de Probabilités IV, Lecture Notes in Math. 124, Springer, Berlin, 1970, 1-27. Zbl0218.60045
  7. [7] R. Cairoli and J. B. Walsh, Stochastic integrals in the plane, Acta Math. 134 (1975), 111-183. Zbl0334.60026
  8. [8] J.-A. Chao and S. Janson, A note on H¹ q-martingales, Pacific J. Math. 97 (1981), 307-317. Zbl0438.60041
  9. [9] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973. 
  10. [10] R. F. Gundy, Inégalités pour martingales à un et deux indices: L’espace H p , in: Ecole d’Eté de Probabilités de Saint-Flour VIII-1978, Lecture Notes in Math. 774, Springer, Berlin, 1980, 251-331. 
  11. [11] R. F. Gundy and N. T. Varopoulos, A martingale that occurs in harmonic analysis, Ark. Mat. 14 (1976), 179-187. Zbl0371.60058
  12. [12] A. Gut, Convergence of reversed martingales with multidimensional indices, Duke Math. J. 43 (1976), 269-275. Zbl0338.60027
  13. [13] C. Metraux, Quelques inégalités pour martingales à paramètre bidimensionnel, in: Séminaire de Probabilités XII, Lecture Notes in Math. 649, Springer, Berlin, 1978, 170-179. Zbl0381.60042
  14. [14] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971. 
  15. [15] F. Schipp, On a generalization of the concept of orthogonality, Acta Sci. Math. (Szeged) 37 (1975), 279-285. Zbl0349.42010
  16. [16] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series: An Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, 1990. Zbl0727.42017
  17. [17] E. M. Stein, Topics in Harmonic Analysis, Princeton Univ. Press, 1970. Zbl0193.10502
  18. [18] F. Weisz, Conjugate martingale transforms, Studia Math. 103 (1992), 207-220. Zbl0809.60056
  19. [19] F. Weisz, Dyadic martingale Hardy and VMO spaces on the plane, Acta Math. Hungar. 56 (1990), 143-154. Zbl0718.60042
  20. [20] F. Weisz, Inequalities relative to two-parameter Vilenkin-Fourier coefficients, Studia Math. 99 (1991), 221-233. Zbl0728.60046
  21. [21] F. Weisz, Martingale Hardy spaces for 0 < p ≤ 1, Probab. Theory Related Fields 84 (1990), 361-376. Zbl0687.60046
  22. [22] F. Weisz, On duality problems of two-parameter martingale Hardy spaces, Bull. Sci. Math. 114 (1990), 395-410. Zbl0746.60048

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.