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1999 | 133 | 3 | 197-230
Tytuł artykułu

Local Hardy spaces on Chébli-Trimèche hypergroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the local Hardy spaces $h^p$ on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.
Słowa kluczowe
Czasopismo
Rocznik
Tom
133
Numer
3
Strony
197-230
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-05-15
poprawiono
1998-08-24
Twórcy
  • Division of Science, Murdoch University Perth, Western Australia 6150, Australia, bloom@murdoch.edu.au
autor
  • Division of Science, Murdoch University Perth, Western Australia 6150, Australia, zengfu@murdoch.edu.au
Bibliografia
  • [A] J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297.
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  • [BH] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Stud. Math. 20, Walter de Gruyter, Berlin, 1995.
  • [BX1] W. R. Bloom and Z. Xu, The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups, in: Applications of Hypergroups and Related Measure Algebras (Joint Summer Research Conference (AMS-IMS-SIAM), Seattle, 1993), Contemp. Math. 183, Amer. Math. Soc., Providence, R.I., 1995, 45-70.
  • [BX2] W. R. Bloom and Z. Xu, Maximal functions on Chébli-Trimèche hypergroups, preprint.
  • [BX3] W. R. Bloom and Z. Xu, Hardy spaces on Chébli-Trimèche hypergroups, Methods Funct. Anal. Topology 3 (1997).
  • [Cha] D. C. Chang, Estimates for singular integral operators with mixed type homogeneities in Hardy classes, Math. Ann. 287 (1990), 303-322.
  • [Ché] H. Chébli, Sur un théorème de Paley-Wiener associé à la décomposition spectrale d'un opérateur de Sturm-Liouville sur ]0,∞[, J. Funct. Anal. 17 (1974), 447-461.
  • [Coi] R. R. Coifman, A real variable characterization of $H^p$, Studia Math. 51 (1974), 269-274.
  • [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 549-645.
  • [FeS] C. Fefferman and E. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
  • [FoS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Math. Notes 28, Princeton Univ. Press, Princeton, N.J., 1982.
  • [G] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42.
  • [GV] R. Gangolli and V. S. Varadarajan, Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb. 101, Springer, Berlin, 1988.
  • [JSW] A. Jonsson, P. Sjögren and H. Wallin, Hardy and Lipschitz spaces on subsets of $ℝ^n$, Studia Math. 80 (1984), 141-166.
  • [K1] T. Kawazoe, Maximal functions on non-compact, rank one symmetric spaces, in: Adv. Stud. Pure Math. 4, Kinokuniya, Tokyo, 1984, 121-138.
  • [K2] T. Kawazoe, Atomic Hardy spaces on semisimple Lie groups, Japan. J. Math. 11 (1985), 293-343.
  • [Lan] R. E. Langer, On the asymptotic solutions of ordinary differential equations, with reference to the Stokes' phenomenon about a singular point, Trans. Amer. Math. Soc. 37 (1935), 397-416.
  • [Lat] R. H. Latter, A characterization of $H^p(ℝ^n)$ in terms of atoms, Studia Math. 62 (1978), 93-101.
  • [MS] R. A. Macias and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. Math. 33 (1979), 271-309.
  • [PS] L. Päivärinta and E. Somersalo, A generalization of the Calderón-Vaillancourt theorem to $L^p$ and $h^p$, Math. Nachr. 138 (1988), 145-156.
  • [T] K. Trimèche, Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur (0,∞), J. Math. Pures Appl. (9) 60 (1981), 51-98.
  • [Z] H. Zeuner, One-dimensional hypergroups, Adv. Math. 76 (1989), 1-18.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv133i3p197bwm
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