The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure

 Access to full text

 Full (PDF)

1. [1] P. Cannarsa – V. Vespri, Generation of analytic semigroups in the $L^p$ topology by elliptic operators in ${ℝ}^n$, Israel J. Math. 61 (1988), 235-255. Zbl0669.35026MR941240
2. [2] A. Chojnowska-Michalik – B. Goldys, Generalized symmetric Ornstein-Uhlenbeck operators in $L^p$: Littlewood-Paley-Stein inequalities and domains of generators, to appear in J. Funct. Anal. MR1828795
3. [3] A. Chojnowska-Michalik – B. Goldys, Symmetric Ornstein-Uhlenbeck generators: Characterizations and identification of domains, preprint. 
4. [4] P. Clément – J. Prüss, Completely positive measures and Feller semigroups, Math. Ann. 287 (1990), 73-105. Zbl0717.47013MR1048282
5. [5] R. R. Coifman – G. Weiss, Transference Methods in Analysis, Amer. Math. Society, 1977. Zbl0377.43001MR481928
6. [6] G. Da Prato, Characterization of the domain of an elliptic operator of infinitely many variables in $L^2\left(\mu \right)$ spaces, Rend. Mat. Acc. Lincei 8 (1997), 101-105. Zbl0899.47035MR1485321
7. [7] G. Da Prato, Perturbation of Ornstein–Uhlenbeck semigroups, Rend. Istit. Mat. Univ. Trieste 28 (1997), 101-126. Zbl0897.60070MR1602247
8. [8] G. Da Prato – A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal. 131 (1995), 94-114. Zbl0846.47004MR1343161
9. [9] G. Da Prato – B. Goldys, On perturbations of symmetric Gaussian diffusions, Stochastic Anal. Appl. 17 (1999), 369-382. Zbl0935.60062MR1686991
10. [10] G. Da Prato – V. Vespri, Maximal $L^p$ regularity for elliptic equations with unbounded coefficients, to appear in Nonlinear Analysis TMA. Zbl1012.35027
11. [11] G. Da Prato – J. Zabczyk, “Stochastic Equations in Infinite Dimensions”, Cambridge University Press, 1992. Zbl0761.60052MR1207136
12. [12] G. Da Prato – J. Zabczyk, Regular densities of invariant measures in Hilbert spaces, J. Funct. Anal. 130 (1995), 427-449. Zbl0832.60069MR1335387
13. [13] G. Dore – A. Venni, On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 189-201. Zbl0615.47002MR910825
14. [14] A. Lunardi, On the Ornstein-Uhlenbeck operator in $L^2$ spaces with respect to invariant measures, Trans. Amer. Math. Soc. 349 (1997), 155-169. Zbl0890.35030MR1389786
15. [15] G. Metafune, $L^p$-spectrum of Ornstein-Uhlenbeck operators, Ann. Sc. Norm. Sup. Pisa 30 (2001), 97-124. Zbl1065.35216MR1882026
16. [16] G. Metafune – D. Pallara – E. Priola, Spectrum of Ornstein-Uhlenbeck operators in $L^p$ spaces with respect to invariant measures, preprint. Zbl1027.47036
17. [17] S. Monniaux – J. Prüss, A theorem of the Dore-Venni type for noncommuting operators, Trans. Amer. Math. Soc. 349 (1997), 4787-4814. Zbl0887.47015MR1433125
18. [18] J. Prüss – H. Sohr, On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429-452. Zbl0665.47015MR1038710
19. [19] J. Prüss – H. Sohr, Imaginary powers of elliptic second order differential operators in $L^p$-space, Hiroshima Math. J. 23 (1993), 161-192. Zbl0790.35023MR1211773
20. [20] I. Shigekawa, Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator, J. Math. Kyoto Univ. 32 (1992), 731-748. Zbl0777.60047MR1194112

1. Robert Haller-Dintelmann, Julian Wiedl, Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator
2. Giancarlo Mauceri, Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck