Conjugate martingale transforms
Weisz, Ferenc
Studia Mathematica, Tome 103 (1992), p. 207-220 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215945
@article{bwmeta1.element.bwnjournal-article-smv103i2p207bwm,
     author = {Ferenc Weisz},
     title = {Conjugate martingale transforms},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {207-220},
     zbl = {0809.60056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i2p207bwm}
}
Weisz, Ferenc. Conjugate martingale transforms. Studia Mathematica, Tome 103 (1992) pp. 207-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i2p207bwm/

[00000] [1] R. Bañuelos, A note on martingale transforms and Ap-weights, Studia Math. 85 (1987), 125-135. | Zbl 0657.42015

[00001] [2] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. | Zbl 0301.60035

[00002] [3] D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249-304. | Zbl 0223.60021

[00003] [4] J. A. Chao, Conjugate characterizations of H¹ dyadic martingales, Math. Ann. 240 (1979), 63-67. | Zbl 0403.42016

[00004] [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.

[00005] [6] J. A. Chao, Hp spaces of conjugate systems on local fields, Studia Math. 49 (1974), 267-287. | Zbl 0247.31014

[00006] [7] J. A. Chao, Lusin area functions on local fields, Pacific J. Math. 59 (1975), 383-390. | Zbl 0313.43017

[00007] [8] J. A. Chao and J. Janson, A note on H¹ q-martingales, ibid. 97 (1981), 307-317. | Zbl 0438.60041

[00008] [9] J. A. Chao and M. H. Taibleson, A sub-regularity inequality for conjugate systems on local fields, Studia Math. 46 (1973), 249-257. | Zbl 0258.46046

[00009] [10] J. A. Chao and M. H. Taibleson, Generalized conjugate systems on local fields, ibid. 64 (1979), 213-225. | Zbl 0414.43003

[00010] [11] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137-194. | Zbl 0257.46078

[00011] [12] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Note Ser., Benjamin, New York 1973.

[00012] [13] R. F. Gundy, Inégalités pour martingales à un et deux indices: L’espace Hp, in: Ecole d’Eté de Probabilités de Saint-Flour VIII-1978, Lecture Notes in Math. 774, Springer, Berlin 1980, 251-331.

[00013] [14] R. F. Gundy and N. T. Varopoulos, A martingale that occurs in harmonic analysis, Ark. Mat. 14 (1976), 179-187. | Zbl 0371.60058

[00014] [15] S. Janson, Characterizations of H¹ by singular integral transforms on martingales and n, Math. Scand. 41 (1977), 140-152. | Zbl 0369.42005

[00015] [16] S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196. | Zbl 0341.43005

[00016] [17] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971.

[00017] [18] F. Schipp, On Lp-norm convergence of series with respect to product systems, Anal. Math. 2 (1976), 49-64. | Zbl 0364.40009

[00018] [19] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series: An Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, 1990. | Zbl 0727.42017

[00019] [20] P. Simon, Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 28 (1985), 87-101. | Zbl 0586.43001

[00020] [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.

[00021] [22] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. | Zbl 0207.13501

[00022] [23] M. H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, Princeton, N.J., 1975.

[00023] [24] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, New York 1986. | Zbl 0621.42001

[00024] [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.

[00025] [26] N. Ya. Vilenkin, On a class of complete orthonormal systems, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400. | Zbl 0036.35601

[00026] [27] F. Weisz, Inequalities relative to two-parameter Vilenkin-Fourier coefficients, Studia Math. 99 (1991), 221-233. | Zbl 0728.60046

[00027] [28] F. Weisz, Martingale Hardy spaces for 0 < p ≤ 1, Probab. Theory Related Fields 84 (1990), 361-376. | Zbl 0687.60046