Conjugate martingale transforms

Ferenc Weisz

Studia Mathematica (1992)

  • Volume: 103, Issue: 2, page 207-220
  • ISSN: 0039-3223

Abstract

top
Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

How to cite

top

Weisz, Ferenc. "Conjugate martingale transforms." Studia Mathematica 103.2 (1992): 207-220. <http://eudml.org/doc/215945>.

@article{Weisz1992,
abstract = {Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.},
author = {Weisz, Ferenc},
journal = {Studia Mathematica},
keywords = {Riesz transforms; Rademacher series; BMO and VMO martingale spaces; Vilenkin systems; conjugate martingale transforms},
language = {eng},
number = {2},
pages = {207-220},
title = {Conjugate martingale transforms},
url = {http://eudml.org/doc/215945},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Weisz, Ferenc
TI - Conjugate martingale transforms
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 2
SP - 207
EP - 220
AB - Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.
LA - eng
KW - Riesz transforms; Rademacher series; BMO and VMO martingale spaces; Vilenkin systems; conjugate martingale transforms
UR - http://eudml.org/doc/215945
ER -

References

top
  1. [1] R. Bañuelos, A note on martingale transforms and A p -weights, Studia Math. 85 (1987), 125-135. Zbl0657.42015
  2. [2] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. Zbl0301.60035
  3. [3] D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249-304. Zbl0223.60021
  4. [4] J. A. Chao, Conjugate characterizations of H¹ dyadic martingales, Math. Ann. 240 (1979), 63-67. Zbl0403.42016
  5. [5] J. A. Chao, Hardy spaces on regular martingales, in: Martingale Theory in Harmonic Analysis and Banach Spaces, Lecture Notes in Math. 939, Springer, Berlin 1982, 18-28. 
  6. [6] J. A. Chao, H p spaces of conjugate systems on local fields, Studia Math. 49 (1974), 267-287. Zbl0247.31014
  7. [7] J. A. Chao, Lusin area functions on local fields, Pacific J. Math. 59 (1975), 383-390. Zbl0313.43017
  8. [8] J. A. Chao and J. Janson, A note on H¹ q-martingales, ibid. 97 (1981), 307-317. Zbl0438.60041
  9. [9] J. A. Chao and M. H. Taibleson, A sub-regularity inequality for conjugate systems on local fields, Studia Math. 46 (1973), 249-257. Zbl0258.46046
  10. [10] J. A. Chao and M. H. Taibleson, Generalized conjugate systems on local fields, ibid. 64 (1979), 213-225. Zbl0414.43003
  11. [11] C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-194. Zbl0257.46078
  12. [12] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Note Ser., Benjamin, New York 1973. 
  13. [13] 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. 
  14. [14] R. F. Gundy and N. T. Varopoulos, A martingale that occurs in harmonic analysis, Ark. Mat. 14 (1976), 179-187. Zbl0371.60058
  15. [15] S. Janson, Characterizations of H¹ by singular integral transforms on martingales and n , Math. Scand. 41 (1977), 140-152. Zbl0369.42005
  16. [16] S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196. Zbl0341.43005
  17. [17] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971. 
  18. [18] F. Schipp, On L p -norm convergence of series with respect to product systems, Anal. Math. 2 (1976), 49-64. Zbl0364.40009
  19. [19] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series: An Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, 1990. Zbl0727.42017
  20. [20] P. Simon, Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 28 (1985), 87-101. Zbl0586.43001
  21. [21] P. Simon, On the concept of a conjugate function, in: Fourier Analysis and Approximation Theory, Budapest 1978, Colloq. Math. Soc. J. Bolyai 1, 747-755. 
  22. [22] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
  23. [23] M. H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, Princeton, N.J., 1975. 
  24. [24] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, New York 1986. Zbl0621.42001
  25. [25] A. Uchiyama, A constructive proof of the Fefferman-Stein decomposition of BMO on simple martingales, in: Conference on Harmonic Analysis in Honor of Antoni Zygmund, Chicago 1981, W. Beckner, A. Calderón, R. Fefferman and P. W. Jones (eds.), Wadsworth, Belmont, Calif., 1983, 495-505. 
  26. [26] N. Ya. Vilenkin, On a class of complete orthonormal systems, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400. Zbl0036.35601
  27. [27] F. Weisz, Inequalities relative to two-parameter Vilenkin-Fourier coefficients, Studia Math. 99 (1991), 221-233. Zbl0728.60046
  28. [28] F. Weisz, Martingale Hardy spaces for 0 < p ≤ 1, Probab. Theory Related Fields 84 (1990), 361-376. Zbl0687.60046

NotesEmbed ?

top

You must be logged in to post comments.