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1997 | 124 | 3 | 215-238
Tytuł artykułu

Besov spaces on symmetric manifolds—the atomic decomposition

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give the atomic decomposition of the inhomogeneous Besov spaces defined on symmetric Riemannian spaces of noncompact type. As an application we get a theorem of Bernstein type for the Helgason-Fourier transform.
Słowa kluczowe
Czasopismo
Rocznik
Tom
124
Numer
3
Strony
215-238
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-01-26
poprawiono
1996-12-12
Twórcy
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49 60-769 Poznań, Poland , lskrzyp@math.amu.edu.pl
Bibliografia
  • [1] J.-P. Anker, $L_p$-Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. 132 (1990), 597-628.
  • [2] J.-P. Anker, The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan, J. Funct. Anal. 96 (1991), 331-349.
  • [3] H. Q. Bui, Representation theorems and atomic decomposition of Besov spaces, Math. Nachr. 132 (1987), 301-311.
  • [4] M. Eguchi, Asymptotic expansions of Eisenstein integrals and Fourier transform on symmetric spaces, J. Funct. Anal. 34 (1979), 164-216.
  • [5] H. G. Feichtinger and K. Gröchenig, A unified approach to atomic decompositions via integrable group representations, in: Function Spaces and Applications, Proc. Conf. Lund 1986, Lecture Notes in Math. 1302, Springer, 1988, 52-73.
  • [6] H. G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, I, J. Funct. Anal. 86 (1989), 307-340; II, Monatsh. Math. 108 (1989), 129-148.
  • [7] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
  • [8] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
  • [9] M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and Study of Function Spaces, CBMS Regional Conf. Ser. in Math. 79, Amer. Math. Soc., 1991.
  • [10] R. Gangolli and V. S. Varadarajan, Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb. 101, Springer, 1988.
  • [11] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, 1978.
  • [12] S. Helgason, Groups and Geometric Analysis. Integral Geometry, Invariant Differential Operators, and Spherical Functions, Academic Press, 1984.
  • [13] S. Helgason, The surjectivity of invariant differential operators on symmetric spaces I, Ann. of Math. 98 (1973), 451-480.
  • [14] T. Kawazoe, Atomic Hardy spaces on semisimple Lie groups, in: Non-Commutative Harmonic Analysis and Lie Groups, Proc. Conf. Marseille 1985, Lecture Notes in Math. 1243, Springer, 1987, 189-197.
  • [15] R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. in Math. 33 (1979), 271-309.
  • [16] L. Skrzypczak, Some equivalent norms in Sobolev and Besov spaces on symmetric manifolds, J. London Math. Soc. 53 (1996), 569-581.
  • [17] L. Skrzypczak, Vector-valued Fourier multipliers on symmetric spaces of the noncompact type, Monatsh. Math. 119 (1995), 99-123.
  • [18] H. Triebel, Atomic decomposition of $F^s_p,q$ spaces. Applications to exotic pseudodifferential and Fourier integral operators, Math. Nachr. 144 (1989), 189-222.
  • [19] H. Triebel, How to measure smoothness of distributions on Riemannian symmetric manifolds and Lie groups?, Z. Anal. Anwendungen 7 (1988), 471-480.
  • [20] H. Triebel, Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds, Ark. Mat. 24 (1986), 300-337.
  • [21] H. Triebel, Theory of Function Spaces II, Birkhäuser, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-smv124i3p215bwm
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