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

Waldemar Hebisch

Colloquium Mathematicae (1997)

  • Volume: 73, Issue: 1, page 155-164
  • ISSN: 0010-1354

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Hebisch, Waldemar. "Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group." Colloquium Mathematicae 73.1 (1997): 155-164. <http://eudml.org/doc/210474>.

@article{Hebisch1997,
author = {Hebisch, Waldemar},
journal = {Colloquium Mathematicae},
keywords = {elliptic laplacian; solvable unimodular group; operator},
language = {eng},
number = {1},
pages = {155-164},
title = {Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group},
url = {http://eudml.org/doc/210474},
volume = {73},
year = {1997},
}

TY - JOUR
AU - Hebisch, Waldemar
TI - Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group
JO - Colloquium Mathematicae
PY - 1997
VL - 73
IS - 1
SP - 155
EP - 164
LA - eng
KW - elliptic laplacian; solvable unimodular group; operator
UR - http://eudml.org/doc/210474
ER -

References

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  1. [1] G. Alexopoulos, Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math. Soc. 120 (1994), 973-979. Zbl0794.43003
  2. [2] J.-Ph. Anker, L p Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. 132 (1990), 597-628. Zbl0741.43009
  3. [3] J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297. Zbl0764.43005
  4. [4] M. Christ, L p bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81. Zbl0739.42010
  5. [5] M. Christ and D. Müller, On L p spectral multipliers for a solvable Lie group, preprint. 
  6. [6] M. Christ and C. Sogge, The weak type L 1 convergence of eigenfunction expansions for pseudodifferential operators, Invent. Math. 94 (1988), 421-453. Zbl0678.35096
  7. [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. Zbl0296.43004
  8. [8] M. Cowling, Harmonic analysis on semigroups, Ann. of Math. 117 (1983), 267-283. Zbl0528.42006
  9. [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. Zbl0820.43001
  10. [10] W. Hebisch, The subalgebra of L 1 ( A N ) generated by the laplacian, Proc. Amer. Math. Soc. 117 (1993), 547-549. Zbl0789.22018
  11. [11] W. Hebisch, Multiplier theorem on generalized Heisenberg groups, Colloq. Math. 65 (1993), 231-239. Zbl0841.43009
  12. [12] W. Hebisch and J. Zienkiewicz, Multiplier theorem on generalized Heisenberg groups II, ibid. 69 (1995), 29-36. Zbl0835.43009
  13. [13] L. Hörmander, Estimates for translation invariant operators in L p spaces, Acta Math. 104 (1960), 93-140. Zbl0093.11402
  14. [14] A. Hulanicki, Subalgebra of L 1 ( G ) associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. Zbl0316.43005
  15. [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. Zbl0461.47018
  16. [16] G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 6 (1990), 141-154. Zbl0763.43005
  17. [17] D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl. 73 (1994), 413-440. Zbl0838.43011
  18. [18] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, Princeton, 1970. Zbl0193.10502
  19. [19] M. Taylor, L p -Estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), 773-793. 
  20. [20] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, 1980. 

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