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1997 | 73 | 1 | 155-164
Tytuł artykułu

Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
73
Numer
1
Strony
155-164
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-02-20
poprawiono
1996-06-20
poprawiono
1996-11-06
Twórcy
  • Institute of Mathematics, Wrocław Uniwersity, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] G. Alexopoulos, Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math. Soc. 120 (1994), 973-979.
  • [2] J.-Ph. Anker, $L_p$ Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. 132 (1990), 597-628.
  • [3] J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297.
  • [4] M. Christ, $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81.
  • [5] M. Christ and D. Müller, On $L^p$ spectral multipliers for a solvable Lie group, preprint.
  • [6] M. Christ and C. Sogge, The weak type $L^1$ convergence of eigenfunction expansions for pseudodifferential operators, Invent. Math. 94 (1988), 421-453.
  • [7] J. L. Clerc and E. M. Stein, $L^p$-multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911-3912.
  • [8] M. Cowling, Harmonic analysis on semigroups, Ann. of Math. 117 (1983), 267-283.
  • [9] M. Cowling, S. Giulini, A. Hulanicki and G. Mauceri, Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth, Studia Math. 111 (1994), 103-121.
  • [10] W. Hebisch, The subalgebra of $L^1(AN)$ generated by the laplacian, Proc. Amer. Math. Soc. 117 (1993), 547-549.
  • [11] W. Hebisch, Multiplier theorem on generalized Heisenberg groups, Colloq. Math. 65 (1993), 231-239.
  • [12] W. Hebisch and J. Zienkiewicz, Multiplier theorem on generalized Heisenberg groups II, ibid. 69 (1995), 29-36.
  • [13] L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104 (1960), 93-140.
  • [14] A. Hulanicki, Subalgebra of $L_1(G)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
  • [15] T. Kato, Trotter's formula for an arbitrary pair of self-adjoint contraction semigroups, in: I. Gohberg and M. Kac (eds.), Topics in Functional Analysis, Academic Press, New York, 1978, 185-195.
  • [16] G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 6 (1990), 141-154.
  • [17] D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl. 73 (1994), 413-440.
  • [18] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, Princeton, 1970.
  • [19] M. Taylor, $L^p$-Estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), 773-793.
  • [20] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv73i1p155bwm
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