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Weak martingale hardy spaces

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Języki publikacji
EN
Abstrakty
EN
Weak martingale Hardy spaces generated by an operator T are investigated. The concept of weak atoms is introduced and an atomic decomposition of the space wHTp is given if the operator T is predictable. Martingale inequalities between weak Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation, and for the conditional q-variation. The duals of the weak Hardy spaces generated by these special operators are characterized.
Rocznik
Strony
133--148
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
  • Department of Numerical Analysis, Eötvös L. University, H-1088 Budapest, Múzeum krt. 6-8, Hungary
Bibliografia
  • [1] J. Bergh and X Löfström, Interpolation Spaces. An Introduction, Springer, Berlin-Heidelberg-New York 1976.
  • [2] A. Bernard et B, Maisonneuve, Decomposition atomique de martingales de la classe H1, in: Séminaire de Probabilités XI, Lecture Notes in Math. 581, Springer, 1977, pp. 303-323.
  • [3] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), pp. 19-42.
  • [4] — and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), pp. 249-304.
  • [5] L. Chevalier, Demonstration atomique des inégalités de Burkholder-Davis-Gundy, Ann. Sd. Univ. Clermont 67 (1979), pp. 19-24.
  • [6] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), pp. 569-645.
  • [7] B. J. Davis, On the integrability of the martingale square function, Israel J. Math. 8 (1970), pp. 187-190.
  • [8] R. Fefferman and F. Soria, The space weak H1, Studia Math. 85 (1987), pp. 1-16.
  • [9] A. M. Qarsia, Martingale inequalities, in: Seminar Notes on Recent Progress, Math. Lecture . Ñote Ser., Benjamin Inc., New York 1973.
  • [10] C. Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), pp. 199-215.
  • [11] — Hp-spaces of martingales, 0 < p ≤ 1, Z. Wahrsch. verw. Gebiete 28 (1974), pp. 189-205.
  • [12] D. Lepingle, La variation d’ordre p des semi-martingales, ibidem 36 (1976), pp. 295-316.
  • [13] — Quelques inégalités concernant les martingales, Studia Math. 59 (1976), pp. 63-83.
  • [14] J. Neveu, Discrete-parameter Martingales, North-Holland, 1971.
  • [15] G. Pisier and Q. Xu, The strong p-variation of martingales and orthogonal series, Probab. Theory Related Fields 77 (1988), pp. 497-514.
  • [16] M. Pratelli, Sur certains espaces de martingales localement de carré integrable, in: Séminaire de Probabilités X, Lecture Notes in Math. 511, Springer, 1976, pp. 401-413.
  • [17] F. Weisz, Martingale Hardy spaces and their applications in Fourier-analysis, Lecture Notes in Math. 1568, Springer, 1994.
  • [18] — Martingale Hardy spaces for 0
  • [19] —Martingale operators and Hardy spaces generated by them, Studia Math. 114 (1995), pp. 39-70.
  • [20] —On duality problems of two-parameter martingale Hardy spaces, Bull. Sei. Math. 114 (1990), pp. 395-410.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9de171d4-5da2-4f06-9df8-a6d078253926
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