Boundedness of L1 spectral multipliers for an exponential solvable Lie group
Hebisch, Waldemar
Colloquium Mathematicae, Tome 72 (1997), p. 155-164 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:210474 
@article{bwmeta1.element.bwnjournal-article-cmv73i1p155bwm,
     author = {Waldemar Hebisch},
     title = {Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {155-164},
     zbl = {0874.22005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p155bwm}
}

Hebisch, Waldemar. Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group. Colloquium Mathematicae, Tome 72 (1997) pp. 155-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p155bwm/

[000] [1] G. Alexopoulos, Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math. Soc. 120 (1994), 973-979. | Zbl 0794.43003

[001] [2] J.-Ph. Anker, Lp Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. 132 (1990), 597-628. | Zbl 0741.43009

[002] [3] J.-Ph. Anker, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J. 65 (1992), 257-297. | Zbl 0764.43005

[003] [4] M. Christ, Lp bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), 73-81. | Zbl 0739.42010

[004] [5] M. Christ and D. Müller, On Lp spectral multipliers for a solvable Lie group, preprint.

[005] [6] M. Christ and C. Sogge, The weak type L1 convergence of eigenfunction expansions for pseudodifferential operators, Invent. Math. 94 (1988), 421-453. | Zbl 0678.35096

[006] [7] J. L. Clerc and E. M. Stein, Lp-multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911-3912. | Zbl 0296.43004

[007] [8] M. Cowling, Harmonic analysis on semigroups, Ann. of Math. 117 (1983), 267-283. | Zbl 0528.42006

[008] [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. | Zbl 0820.43001

[009] [10] W. Hebisch, The subalgebra of L1(AN) generated by the laplacian, Proc. Amer. Math. Soc. 117 (1993), 547-549. | Zbl 0789.22018

[010] [11] W. Hebisch, Multiplier theorem on generalized Heisenberg groups, Colloq. Math. 65 (1993), 231-239. | Zbl 0841.43009

[011] [12] W. Hebisch and J. Zienkiewicz, Multiplier theorem on generalized Heisenberg groups II, ibid. 69 (1995), 29-36. | Zbl 0835.43009

[012] [13] L. Hörmander, Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93-140. | Zbl 0093.11402

[013] [14] A. Hulanicki, Subalgebra of L1(G) associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. | Zbl 0316.43005

[014] [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. | Zbl 0461.47018

[015] [16] G. Mauceri and S. Meda, Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana 6 (1990), 141-154. | Zbl 0763.43005

[016] [17] D. Müller and E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl. 73 (1994), 413-440. | Zbl 0838.43011

[017] [18] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, Princeton, 1970. | Zbl 0193.10502

[018] [19] M. Taylor, Lp-Estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), 773-793.

[019] [20] J. Weidmann, Linear Operators in Hilbert Spaces, Springer, 1980.