Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck

 Access to full text

 Full (PDF)

 Full (DjVu)

1. ALEXOPOULOS, G., Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math., 120 (1991), 973-979. Zbl0794.43003MR1172944
2. ANKER, J.-P., $L^p$ Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. of Math. (2), 123, no. 3 (1990), 597-628. Zbl0741.43009MR1078270
3. ANKER, J.-P., Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke Math. J., 65, no. 2 (1992), 257-297. Zbl0764.43005MR1150587
4. ANKER, J.-P.- LOHOUÉ, N., Multiplicateurs sur certains espaces symetriques, Amer. J. Math., 108 (1986), 1303-1353. Zbl0616.43009MR868894
5. ARENDT, W., Gaussian estimates and interpolation of the spectrum in $L^p$, Differential Integral Equations, 7, no. 5-6 (1994), 1153-1168. Zbl0827.35081MR1269649
6. ASTENGO, F., A. class of $L^p$ convolutors on harmonic extensions of $H$-type groups, J. Lie Theory, 5, no. 2 (1995), 147-164. Zbl0849.43001MR1389425
7. BAKRY, D., 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. Zbl0856.47026MR1307413
8. BOIDOL, J., $*$-Regularity of exponential Lie groups, Invent. Math., 56 (1980), 31-238. Zbl0423.22008MR561972
9. CHOJNOWSKA-MICHALIK, A.- GOLDYS, B., Symmetric Ornstein-Uhlenbeck semigroups and their generators, Probab. Theory Related Fields, 124, no. 4 (2002), 459-486. Zbl1028.60057MR1942319
10. CHRIST, M.- MÜLLER, D., On $L^p$ spectral multipliers for a solvable Lie group, Geom. Funct. Anal., 6 (1996), 860-876. Zbl0878.43008MR1415763
11. CLERC, J.-L.- STEIN, E. M., $L^p$ multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 3911-3912. Zbl0296.43004MR367561
12. CHRIST, M., $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328 (1991), 73-81. Zbl0739.42010MR1104196
13. COIFMAN, R. R.- WEISS, G., Analyse harmonique non-commutative sur certains espaces homognes. Étude de certaines intégrales singulières, Lecture Notes in Mathematics, Vol. 242. Zbl0224.43006MR499948
14. COWLING, M., Harmonic analysis on semigroups, Ann. of Math., 117 (1983), 267-283. Zbl0528.42006MR690846
15. COWLING, M.- DOUST, I.- MCINTOSH, A.- YAGI, A., Banach space operators with a bounded $H^{\mathrm{\infty }}$ functional calculus, J. Austral. Math. Soc., 60 (1996), 51-89. Zbl0853.47010MR1364554
16. COWLING, M.- GIULINI, S.- GAUDRY, G.- MAUCERI, G., Weak type $\left(1,1\right)$ estimates for heat kernel maximal functions in Lie groups, Trans. Amer. Math. Soc., 323 (1991), 637-649. Zbl0722.22006MR967310
17. COWLING, M.- GIULINI, S.- HULANICKI, A.- MAUCERI, G., Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth, Studia Mathematica, 111 (1994), 103-121. Zbl0820.43001MR1301761
18. COWLING, M.- SIKORA, A., A spectral multiplier theorem on $SU\left(2\right)$, Math. Z., 238 (2001), 1-36. Zbl0996.42006MR1860734
19. DA PRATO, G.- ZABCYK, J., Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, 229, Cambridge University Press, Cambridge, 1996. Zbl0849.60052MR1417491
20. DAVIES, E. B., Heat Kernels and Spectral Theory, Cambridge Tract in Math., 92, Cambridge University Press, Cambridge, 1989. Zbl0699.35006MR990239
21. DE MICHELE, L.- MAUCERI, G., $L^p$ multipliers on the Heisenberg group, Michigan Math. J., 26 (1979), 361-371. Zbl0437.43005MR544603
22. DE MICHELE, L.- MAUCERI, G., $H^p$ multipliers on stratified groups, Ann. Mat. Pura Appl., 148 (1987), 353-366. Zbl0638.43007MR932770
23. DUREN, P. L., Theory of $H^p$ spaces, Pure and Applied Math., 38, Academic Press, New York, 1970. Zbl0215.20203MR268655
24. EPPERSON, J. B., The hypercontractive approach to exactly bounding an operator with complex gaussian kernel, J. Funct. Anal., 87 (1989), 1-30. Zbl0696.47028MR1025881
25. FOLLAND, G. B.- STEIN, E. M., Hardy spaces on homogeneous groups, Mathematical Notes, 28, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. Zbl0508.42025
26. GARCIA-CUERVA, J.- MAUCERI, G.- SJÖGREN, P.- TORREA, J. L., Spectral multipliers for the Ornstein-Uhlenbeck semigroup, J. D'Analyse Math., 78 (1999), 281-305. Zbl0939.42007MR1714425
27. GARCIA-CUERVA, J.- MAUCERI, G.- MEDA, S.- SJÖGREN, P.- TORREA, J. L., Functional calculus for the Ornstein-Uhlenbeck operator, J. Funct. Anal., 183 (2001), 413-450. Zbl0995.47010MR1844213
28. GIULINI, S.- MAUCERI, G.- MEDA, S., $L^p$ multipliers on noncompact symmetric spaces, J. Reine Angew. Math., 482 (1997), 151-175. Zbl0860.43004MR1427660
29. HEBISCH, W., A multiplier theorem for Schrödinger operators, Colloq. Math., 60/61 (1990), 659-661. Zbl0779.35025MR1096404
30. HEBISCH, W., The subalgebra of $L^1\left(AN\right)$ generated by the Laplacean, Proc. Amer. Math. Soc., 17 (1993), 547-549. Zbl0789.22018MR1111218
31. HEBISCH, W., Multiplier theorem on generalized Heisenberg groups, Colloq. Math., 65 (1993), 231-239. Zbl0841.43009MR1240169
32. HEBISCH, W., Spectral multipliers on exponential growth solvable Lie groups, Math. Zeitschr., 229 (1998), 435-441. Zbl0946.22010MR1658573
33. HEBISCH, W.- MAUCERI, G.- MEDA, S., Holomorphy of spectral multipliers of the Ornstein-Uhlenbeck operator, in stampa su J. Funct. Anal. Zbl1069.47017MR2052115
34. HEBISCH, W.- LUDWIG, J.- MULLER, D., Sub-Laplacians of holomorphic $L^p$-type on exponential solvable groups, arXiv:math.CA/0307051. Zbl1086.22006
35. HELGASON, S., Groups and geometric analysis, Integral geometry, invariant differential operators, and spherical functions, Mathematical Surveys and Monographs83, American Mathematical Society, Providence, RI, 2000. Zbl0965.43007MR1790156
36. HÖRMANDER, L., Estimates for translation invariant operators in $L^p$ spaces, Acta Math., 104 (1960), 93-140. Zbl0093.11402MR121655
37. IONESCU, A., Singular integrals on symmetric spaces of real rank one, Duke Math. J., 114, no. 1 (2002), 101-122. Zbl1007.43010MR1915037
38. IONESCU, A., Singular integrals on symmetric spaces II, Trans. Amer. Math. Soc., 355, no. 8 (2003), 3359-3378. Zbl1014.22012MR1974692
39. KALTON, N.- WEIS, L., The $H^{\mathrm{\infty }}$-calculus and sums of closed operators, Math. Ann., 321 (2001), 319-345. Zbl0992.47005MR1866491
40. KUNSTMANN, P. C.- STRKALJI, Z., $H^{\mathrm{\infty }}$-calculus for submarkovian generators, Proc. Amer. Math. Soc., 131, no. 7 (2003), 2081-2088. Zbl1031.47012MR1963753
41. LARSON-COHN, L., $L^p$-norms of Hermite polynomials and an extremal problem on Wiener chaos, Ark. Math., 40, no. 1 (2002), 133-144. Zbl1021.60043MR1948890
42. LUDWIG, J.- MÜLLER, D., Sub-Laplacians of holomorphic $L^p$ type on rank one $AN$-groups and related solvable groups, J. Funct. Anal., 170 (2000), 366-427. Zbl0957.22013MR1740657
43. LISKEVICH, V. A.- PERELMUTER, M. A., Analyticity of submarkovian semigroups, Proc. Amer. Math. Soc., 123 (1995), 1097-1104. Zbl0826.47030MR1224619
44. LOHOUÉ, N.- RYCHENER, T., Die Resolvente von $\mathrm{\Delta }$ auf symmetrischen Räumen von nichtkompakten Typ, Comment. Math. Helv., 57, no. 3 (1982), 445-468. Zbl0505.53022MR689073
45. MAUCERI, G., Zonal multipliers on the Heisenberg group, Pacific J. Math., 95 (1981), 143-159. Zbl0474.43009MR631666
46. MAUCERI, G., The Weyl transform and bounded operators on $L^p\left({\mathbb{R}}^n\right)$, J. Funct. Anal., 39 (1980), 408-429. Zbl0458.42008MR600625
47. MAUCERI, G.- MEDA, S., Vector valued inequalities on stratified groups, Rev. Math. Iberoamericana, 6 (1990), 141-154. Zbl0763.43005MR1125759
48. MAUCERI, G.- MEDA, S.- SJÖGREN, P., Sharp estimates for the Ornstein-Uhlenbeck operator, preprint. Zbl1116.47036MR2099246
49. MEDA, S., A general multiplier theorem, Proc. Amer. Math. Soc., 110 (1990), 639-647. Zbl0760.42007MR1028046
50. METAFUNE, G.- PALLARA, D.- PRIOLA, E., Spectrum of Ornstein-Uhlenbeck operators in $L^p$ spaces with respect to invariant measures, J. Funct. Anal., 196, no. 1 (2002), 40-60. Zbl1027.47036MR1941990
51. METAFUNE, G.- PRÜSS, J.- RHANDI, A.- SCHNAUBELT, R., 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. Zbl1170.35375MR1991148
52. MEYER, P. A., Notes sur le processus d'Ornstein-Uhlenbeck, Springer Lecture Notes in Mathematics, 920 (1982), 95-132. Zbl0481.60041MR658673
53. MIHLIN, S. G., On the multipliers of Fourier integrals, Dok. Akad. Nauk., 109 (1956), 701-703. Zbl0073.08402MR80799
54. MÜLLER, D.- STEIN, E. M., On spectral multipliers for the Heisenberg and related groups, J. Math. Pures Appl., 73 (1994), 413-440. Zbl0838.43011MR1290494
55. NELSON, E., The free Markov field, J. Funct. Anal., 12 (1973), 211-227. Zbl0273.60079MR343816
56. PISIER, G., Riesz transform: a simpler analytic proof of P. A. Meyer's inequality, Springer Lectures Notes in Mathematics, 1321 (1988), 485-501. Zbl0645.60061MR960544
57. REED, M.- SIMON, B., Methods of Modern Mathematical Physics. Vol. I. Functional Analysis, Revised and enlarged edition, Academic Press, New York, 1980. Zbl0459.46001MR751959
58. SASSO, E., Functional Calculus for the Laguerre Operator, preprint. Zbl1071.47020MR2121746