Riesz means on Lie groups and riemannian manifolds of nonnegative curvature

Alexopoulos, Georgios; Lohoué, Noël

Bulletin de la Société Mathématique de France, Tome 122 (1994) no. 2, pp. 209-223.

[1] Alexopoulos (G.). - Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math. Soc., (to appear). | Zbl

[2] Berard (P.). - Riesz means on Riemannian manifolds, Proc. Sympos. Pure Math., t. 36, 1980, p. 1-12. | MR | Zbl

[3] Bishop (R.) and Crittenden (R.). - Geometry of manifolds. - Academic Press, New York, 1964. | MR | Zbl

[4] Cheeger (J.) and Gromoll (D.). - The structure of complete manifolds of nonnegative curvature, Bull. Amer. Math. Soc., t. 74, 6, 1968, p. 413-443. | MR | Zbl

[5] Cheeger (J.), Gromov (M.) and Taylor (M.). - Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds, J. Differential Geom., t. 17, 1982, p. 15-53. | MR | Zbl

[6] Christ (M.). - Lp bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., t. 328, 1, 1991, p. 73-81. | MR | Zbl

[7] Christ (M.). - Weak type (1,1) bounds for rough operators, Ann. of Math. (2), t. 128, 1988, p. 19-42. | MR | Zbl

[8] Christ (M.). - Weak type endpoint bounds for Bochner-Riesz operators, Rev. Mat. Iberoamericana, t. 3, 1987, p. 25-31. | MR | Zbl

[9] Christ (M.) and Sogge (C.). - Weak type L1 convergebce of eigenfunction expansions for pseudodifferential operators, Invent. Math., t. 94, 1988, p. 421-453. | MR | Zbl

[10] Clerc (J.-L.). - Sommes de Riesz et multiplicateurs sur un groupe de Lie compact, Ann. Inst. Fourier, t. 24, 1974, p. 149-172. | Numdam | MR | Zbl

[11] Cowling (M.G.). - Harmonic analysis on semigroups, Ann. of Math., t. 117, 1983, p. 267-283. | MR | Zbl

[12] Davies (E.B.). - Gausian upper bounds for the heat kernels of some second order differential operators on Riemannian manifolds, J. Funct. Anal., t. 80, 1988, p. 16-32. | MR | Zbl

[13] Davis (K.M.) and Chang (Y.-C.). - Lectures on Bochner-Riesz Means, London Mathematical Society Lecture Notes Series, vol. 114, Cambridge University Press. | MR | Zbl

[14] Folland (G.B.) and Stein (E.). - Hardy spaces on Homogeneous groups. - Princeton University Press, N.J., 1982. | MR | Zbl

[15] Giulini (L.) and Mauceri (G.). - Almost everywhere convergence of Riesz means on certain noncompact symmetric spaces, Ann. Mat. Pura Appl. (6), t. CLIX, 1991, p. 357-369. | MR | Zbl

[16] Giulini (L.) and Travaglini (G.). - Estimates for Riesz kernels of eigenfunction expansions of elliptic differential operators on compact manifolds, J. Funct. Anal., t. 96, 1991, p. 1-30. | MR | Zbl

[17] Guivarc'H (Y.). - Croissance polynômiale et périodes de fonctions harmoniques, Bull. Soc. Math. France, t. 101, 1973, p. 149-152. | Numdam | MR | Zbl

[18] Hörmander (L.). - On the Riesz means of spectral functions and eigenfunction expansions for elliptic differenrial operators, Some Recent Advances in the Basic Sciences, p. 155-202, Yeshiva University, New York, 1966.

[19] Hulanicki (A.) and Jenkins (J.-W.). - Almost everywhere summability on nilmanifolds, Trans. Amer. Math. Soc., t. 278, 1983, p. 703-715. | MR | Zbl

[20] Li (P.) and Yau (S.T.). - On the parabolic kernel of the Schrödinger operator, Acta Math., t. 156, 1986, p. 153-201. | MR | Zbl

[21] Mauceri (G.). - Maximal operators and Riesz means on stratified groups, Sympos. Math., t. 29, 1984, p. 47-62. | MR | Zbl

[22] Mauceri (G.) and Meda (S.). - Vector-valued multipliers on stratified groups, Rev. Mat. Iberoamericana, t. 6, 1990, p. 141-154. | MR | Zbl

[23] Melrose (R.). - Propagation for the wave group of a positive subelliptic second order differential operator, Proceedings Tanigushi International Symposium, Katata and Kyoto, S. Mizohata ed., 1984, p. 181-192. | MR | Zbl

[24] Nagel (A.), Stein (E.) and Wainger (S.). - Balls and metrics defined by vector fields I : Basic properties, Acta Math., t. 155, 1985, p. 103-147. | MR | Zbl

[25] Seeger (A.). - Endpoint estimates for multiplier transformations on compact manifolds, Indiana Univ. Math. J., t. 40, 2, 1991, p. 471-533. | MR | Zbl

[26] Sogge (C.). - On the convergence of Riesz means on compact manifolds, Ann. of Math. (2), t. 126, 1987, p. 439-447. | MR | Zbl

[27] Stein (E.). - Localization and summability of multiple Fourier series, Acta Math., t. 100, 1958, p. 93-147. | MR | Zbl

[28] Stein (E.). - Topics in Harmonic Analysis. - Princeton University Press, N.J., 1970. | Zbl

[29] Stein (E.) and Weiss (G.). - Introduction to Fourier Analysis on Euclidean Spaces. - Princeton University Press, Princeton, 1971. | MR | Zbl

[30] Varopoulos (N.Th.). - Analysis on Lie groups, J. Funct. Anal., t. 76, 2, 1988, p. 346-410. | MR | Zbl

[31] Varopoulos (N.Th.). - Small time gaussian estimates of heat diffusion kernels, part I : The semigroup technique, Bull. Sci. Math. (2), t. 113, 1989, p. 253-277. | Zbl

[32] Varopoulos (N.Th.). - Small time gaussian estimates of heat diffusion kernels, part II : The theory of large deviations, J. Funct. Anal., t. 93, 1, 1990, p. 1-33. | Zbl

[33] Varopoulos (N.Th.), Saloff-Coste (L.) and Coulhon (T.). - Analysis and Geometry on Groups. - Cambridge Tracts in Mathematics.

[34] Yosida (K.). - Functional Analysis. - Springer-Verlag, 1978. | MR