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1992 | 103 | 2 | 207-220
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Conjugate martingale transforms

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EN
Abstrakty
EN
Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.
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autor
  • Department of Numerical Analysis, Eötvös L. University, Bogdánfy U. 10/b, H-1117 Budapest, Hungary
Bibliografia
  • [1] R. Bañuelos, A note on martingale transforms and $A_p$-weights, Studia Math. 85 (1987), 125-135.
  • [2] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42.
  • [3] D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249-304.
  • [4] J. A. Chao, Conjugate characterizations of H¹ dyadic martingales, Math. Ann. 240 (1979), 63-67.
  • [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] J. A. Chao, $H^p$ spaces of conjugate systems on local fields, Studia Math. 49 (1974), 267-287.
  • [7] J. A. Chao, Lusin area functions on local fields, Pacific J. Math. 59 (1975), 383-390.
  • [8] J. A. Chao and J. Janson, A note on H¹ q-martingales, ibid. 97 (1981), 307-317.
  • [9] J. A. Chao and M. H. Taibleson, A sub-regularity inequality for conjugate systems on local fields, Studia Math. 46 (1973), 249-257.
  • [10] J. A. Chao and M. H. Taibleson, Generalized conjugate systems on local fields, ibid. 64 (1979), 213-225.
  • [11] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-194.
  • [12] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Note Ser., Benjamin, New York 1973.
  • [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] R. F. Gundy and N. T. Varopoulos, A martingale that occurs in harmonic analysis, Ark. Mat. 14 (1976), 179-187.
  • [15] S. Janson, Characterizations of H¹ by singular integral transforms on martingales and $ℝ^n$, Math. Scand. 41 (1977), 140-152.
  • [16] S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196.
  • [17] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971.
  • [18] F. Schipp, On $L_p$-norm convergence of series with respect to product systems, Anal. Math. 2 (1976), 49-64.
  • [19] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series: An Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, 1990.
  • [20] P. Simon, Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 28 (1985), 87-101.
  • [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] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
  • [23] M. H. Taibleson, Fourier Analysis on Local Fields, Princeton Univ. Press, Princeton, N.J., 1975.
  • [24] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, New York 1986.
  • [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] N. Ya. Vilenkin, On a class of complete orthonormal systems, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400.
  • [27] F. Weisz, Inequalities relative to two-parameter Vilenkin-Fourier coefficients, Studia Math. 99 (1991), 221-233.
  • [28] F. Weisz, Martingale Hardy spaces for 0 < p ≤ 1, Probab. Theory Related Fields 84 (1990), 361-376.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv103i2p207bwm
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