bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Mauceri, Giancarlo:
Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck
Bollettino dell'Unione Matematica Italiana Serie 8 7-B (2004), fasc. n.3, p. 563-591, Unione Matematica Italiana (Italian)
pdf (543 Kb), djvu (602 Kb). | MR2101652 | Zbl 1182.47038

Sunto

Questa è una rassegna di alcuni risultati recenti sui moltiplicatori spettrali dell'operatore di Ornstein-Uhlenbeck, un laplaciano naturale sullo spazio euclideo munito della misura gaussiana. I risultati sono inquadrati nell'ambito della teoria generale dei moltiplicatori spettrali per laplaciani generalizzati.
Referenze Bibliografiche
[1] G. ALEXOPOULOS, Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math., 120 (1991), 973-979. | MR 1172944 | Zbl 0794.43003
[2] J.-P. ANKER, $L^p$ Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. (2), 123, no. 3 (1990), 597-628. | MR 1078270 | Zbl 0741.43009
[3] J.-P. ANKER, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J., 65, no. 2 (1992), 257-297. | fulltext mini-dml | MR 1150587 | Zbl 0764.43005
[4] J.-P. ANKER-N. LOHOUÉ, Multiplicateurs sur certains espaces symetriques, Amer. J. Math., 108 (1986), 1303-1353. | MR 868894 | Zbl 0616.43009
[5] W. ARENDT, Gaussian estimates and interpolation of the spectrum in $L^p$, Differential Integral Equations, 7, no. 5-6 (1994), 1153-1168. | MR 1269649 | Zbl 0827.35081
[6] F. ASTENGO, A. class of $L^p$ convolutors on harmonic extensions of $H$-type groups, J. Lie Theory, 5, no. 2 (1995), 147-164. | MR 1389425 | Zbl 0849.43001
[7] D. BAKRY, L'hypercontractivité et son utilisation en théorie des semi-groupes, in Lectures on Probability Theory, D. Bakry, R. D. Gill and S. A. Molchanov editors, Springer Lecture Notes in Mathematics, 1581 (1994), 1-114. | MR 1307413 | Zbl 0856.47026
[8] J. BOIDOL, $*$-Regularity of exponential Lie groups, Invent. Math., 56 (1980), 31-238. | MR 561972 | Zbl 0423.22008
[9] A. CHOJNOWSKA-MICHALIK-B. GOLDYS, Symmetric Ornstein-Uhlenbeck semigroups and their generators, Probab. Theory Related Fields, 124, no. 4 (2002), 459-486. | MR 1942319 | Zbl 1028.60057
[10] M. CHRIST-D. MÜLLER, On $L^p$ spectral multipliers for a solvable Lie group, Geom. Funct. Anal., 6 (1996), 860-876. | MR 1415763 | Zbl 0878.43008
[11] J.-L. CLERC-E. M. STEIN, $L^p$ multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 3911-3912. | MR 367561 | Zbl 0296.43004
[12] M. CHRIST, $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328 (1991), 73-81. | MR 1104196 | Zbl 0739.42010
[13] R. R. COIFMAN-G. WEISS, Analyse harmonique non-commutative sur certains espaces homognes. Étude de certaines intégrales singulières, Lecture Notes in Mathematics, Vol. 242. | MR 499948 | Zbl 0224.43006
[14] M. COWLING, Harmonic analysis on semigroups, Ann. of Math., 117 (1983), 267-283. | MR 690846 | Zbl 0528.42006
[15] M. COWLING-I. DOUST-A. MCINTOSH-A. YAGI, Banach space operators with a bounded $H^\infty$ functional calculus, J. Austral. Math. Soc., 60 (1996), 51-89. | MR 1364554 | Zbl 0853.47010
[16] M. COWLING-S. GIULINI-G. GAUDRY-G. MAUCERI, Weak type $(1, 1)$ estimates for heat kernel maximal functions in Lie groups, Trans. Amer. Math. Soc., 323 (1991), 637-649. | MR 967310 | Zbl 0722.22006
[17] M. COWLING-S. GIULINI-A. HULANICKI-G. MAUCERI, Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth, Studia Mathematica, 111 (1994), 103-121. | fulltext mini-dml | MR 1301761 | Zbl 0820.43001
[18] M. COWLING-A. SIKORA, A spectral multiplier theorem on $SU(2)$, Math. Z., 238 (2001), 1-36. | MR 1860734 | Zbl 0996.42006
[19] G. DA PRATO-J. ZABCYK, Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, 229, Cambridge University Press, Cambridge, 1996. | MR 1417491 | Zbl 0849.60052
[20] E. B. DAVIES, Heat Kernels and Spectral Theory, Cambridge Tract in Math., 92, Cambridge University Press, Cambridge, 1989. | MR 990239 | Zbl 0699.35006
[21] L. DE MICHELE-G. MAUCERI, $L^p$ multipliers on the Heisenberg group, Michigan Math. J., 26 (1979), 361-371. | fulltext mini-dml | MR 544603 | Zbl 0437.43005
[22] L. DE MICHELE-G. MAUCERI, $H^p$ multipliers on stratified groups, Ann. Mat. Pura Appl., 148 (1987), 353-366. | MR 932770 | Zbl 0638.43007
[23] P. L. DUREN, Theory of $H^p$ spaces, Pure and Applied Math., 38, Academic Press, New York, 1970. | MR 268655 | Zbl 0215.20203
[24] J. B. EPPERSON, The hypercontractive approach to exactly bounding an operator with complex gaussian kernel, J. Funct. Anal., 87 (1989), 1-30. | MR 1025881 | Zbl 0696.47028
[25] G. B. FOLLAND-E. M. STEIN, Hardy spaces on homogeneous groups, Mathematical Notes, 28, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. | Zbl 0508.42025
[26] J. GARCIA-CUERVA-G. MAUCERI-P. SJÖGREN-J. L. TORREA, Spectral multipliers for the Ornstein-Uhlenbeck semigroup, J. D'Analyse Math., 78 (1999), 281-305. | MR 1714425 | Zbl 0939.42007
[27] J. GARCIA-CUERVA-G. MAUCERI-S. MEDA-P. SJÖGREN-J. L. TORREA, Functional calculus for the Ornstein-Uhlenbeck operator, J. Funct. Anal., 183 (2001), 413-450. | MR 1844213 | Zbl 0995.47010
[28] S. GIULINI-G. MAUCERI-S. MEDA, $L^p$ multipliers on noncompact symmetric spaces, J. Reine Angew. Math., 482 (1997), 151-175. | MR 1427660 | Zbl 0860.43004
[29] W. HEBISCH, A multiplier theorem for Schrödinger operators, Colloq. Math., 60/61 (1990), 659-661. | MR 1096404 | Zbl 0779.35025
[30] W. HEBISCH, The subalgebra of $L^1(AN)$ generated by the Laplacean, Proc. Amer. Math. Soc., 17 (1993), 547-549. | MR 1111218 | Zbl 0789.22018
[31] W. HEBISCH, Multiplier theorem on generalized Heisenberg groups, Colloq. Math., 65 (1993), 231-239. | MR 1240169 | Zbl 0841.43009
[32] W. HEBISCH, Spectral multipliers on exponential growth solvable Lie groups, Math. Zeitschr., 229 (1998), 435-441. | MR 1658573 | Zbl 0946.22010
[33] W. HEBISCH-G. MAUCERI-S. MEDA, Holomorphy of spectral multipliers of the Ornstein-Uhlenbeck operator, in stampa su J. Funct. Anal. | MR 2052115 | Zbl 1069.47017
[34] W. HEBISCH-J. LUDWIG-D. MULLER, Sub-Laplacians of holomorphic $L^p$-type on exponential solvable groups, arXiv:math.CA/0307051. | fulltext mini-dml | Zbl 1086.22006
[35] S. HELGASON, Groups and geometric analysis, Integral geometry, invariant differential operators, and spherical functions, Mathematical Surveys and Monographs 83, American Mathematical Society, Providence, RI, 2000. | MR 1790156 | Zbl 0965.43007
[36] L. HÖRMANDER, Estimates for translation invariant operators in $L^p$ spaces, Acta Math., 104 (1960), 93-140. | MR 121655 | Zbl 0093.11402
[37] A. IONESCU, Singular integrals on symmetric spaces of real rank one, Duke Math. J., 114, no. 1 (2002), 101-122. | fulltext mini-dml | MR 1915037 | Zbl 1007.43010
[38] A. IONESCU, Singular integrals on symmetric spaces II, Trans. Amer. Math. Soc., 355, no. 8 (2003), 3359-3378. | MR 1974692 | Zbl 1014.22012
[39] N. KALTON-L. WEIS, The $H^\infty$-calculus and sums of closed operators, Math. Ann., 321 (2001), 319-345. | MR 1866491 | Zbl 0992.47005
[40] P. C. KUNSTMANN-Z. STRKALJI, $H^\infty$-calculus for submarkovian generators, Proc. Amer. Math. Soc., 131, no. 7 (2003), 2081-2088. | MR 1963753 | Zbl 1031.47012
[41] L. LARSON-COHN, $L^p$-norms of Hermite polynomials and an extremal problem on Wiener chaos, Ark. Math., 40, no. 1 (2002), 133-144. | MR 1948890 | Zbl 1021.60043
[42] J. LUDWIG-D. MÜLLER, Sub-Laplacians of holomorphic $L^p$ type on rank one $AN$-groups and related solvable groups, J. Funct. Anal., 170 (2000), 366-427. | MR 1740657 | Zbl 0957.22013
[43] V. A. LISKEVICH-M. A. PERELMUTER, Analyticity of submarkovian semigroups, Proc. Amer. Math. Soc., 123 (1995), 1097-1104. | MR 1224619 | Zbl 0826.47030
[44] N. LOHOUÉ-T. RYCHENER, Die Resolvente von $\Delta$ auf symmetrischen Räumen von nichtkompakten Typ, Comment. Math. Helv., 57, no. 3 (1982), 445-468. | MR 689073 | Zbl 0505.53022
[45] G. MAUCERI, Zonal multipliers on the Heisenberg group, Pacific J. Math., 95 (1981), 143-159. | fulltext mini-dml | MR 631666 | Zbl 0474.43009
[46] G. MAUCERI, The Weyl transform and bounded operators on $L^p(\mathbb{R}^n)$, J. Funct. Anal., 39 (1980), 408-429. | MR 600625 | Zbl 0458.42008
[47] G. MAUCERI-S. MEDA, Vector valued inequalities on stratified groups, Rev. Math. Iberoamericana, 6 (1990), 141-154. | MR 1125759 | Zbl 0763.43005
[48] G. MAUCERI-S. MEDA-P. SJÖGREN, Sharp estimates for the Ornstein-Uhlenbeck operator, preprint. | MR 2099246 | Zbl 1116.47036
[49] S. MEDA, A general multiplier theorem, Proc. Amer. Math. Soc., 110 (1990), 639-647. | MR 1028046 | Zbl 0760.42007
[50] G. METAFUNE-D. PALLARA-E. PRIOLA, Spectrum of Ornstein-Uhlenbeck operators in $L^p$ spaces with respect to invariant measures, J. Funct. Anal., 196, no. 1 (2002), 40-60. | MR 1941990 | Zbl 1027.47036
[51] G. METAFUNE-J. PRÜSS-A. RHANDI-R. SCHNAUBELT, The domain of the Ornstein-Uhlenbeck operator on an $L^p$-spaces with invariant measure, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 1, no. 2 (2002), 471-485. | fulltext mini-dml | MR 1991148 | Zbl 1170.35375
[52] P. A. MEYER, Notes sur le processus d'Ornstein-Uhlenbeck, Springer Lecture Notes in Mathematics, 920 (1982), 95-132. | fulltext mini-dml | MR 658673 | Zbl 0481.60041
[53] S. G. MIHLIN, On the multipliers of Fourier integrals, Dok. Akad. Nauk., 109 (1956), 701-703. | MR 80799 | Zbl 0073.08402
[54] D. MÜLLER-E. M. STEIN, On spectral multipliers for the Heisenberg and related groups, J. Math. Pures Appl., 73 (1994), 413-440. | MR 1290494 | Zbl 0838.43011
[55] E. NELSON, The free Markov field, J. Funct. Anal., 12 (1973), 211-227. | MR 343816 | Zbl 0273.60079
[56] G. PISIER, Riesz transform: a simpler analytic proof of P. A. Meyer's inequality, Springer Lectures Notes in Mathematics, 1321 (1988), 485-501. | fulltext mini-dml | MR 960544 | Zbl 0645.60061
[57] M. REED-B. SIMON, Methods of Modern Mathematical Physics. Vol. I. Functional Analysis, Revised and enlarged edition, Academic Press, New York, 1980. | MR 751959 | Zbl 0459.46001
[58] E. SASSO, Functional Calculus for the Laguerre Operator, preprint. | MR 2121746 | Zbl 1071.47020

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali