On a Dirichlet Problem Involving an Ornstein-Uhlenbeck Operator

Potential Analysis

Volumn 18, Issue 3, 2003, Pages 251-287

  Priola, Enrico ^a  

^a UNIVERSITY OF TURIN   (Italy)

Author keywords

Ornstein Uhlenbeck semigroup; Poisson kernels; Real interpolation spaces; Schauder estimates; Subordination of semigroups

Indexed keywords

EID: 0037210038     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020933325029     Document Type: Article

References (38)

1. Aronson, D.G. and Besala, P.: 'Parabolic Equations with unbounded coefficients', J. Differential Equations 3 (1967), 1-14.
2. Barucci, E., Gozzi, F. and Vespri, V.: 'On a semigroup approach to no-arbitrage pricing theory', in Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), Progr. Probab. 45, Birkhäuser, 1999, pp. 1-14.
3. Besala, P.: 'On the existence of a foundamental solution for a parabolic equation with unbounded coefficients', Ann. Polon. Math. 29 (1975), 403-409.
4. Bochner, S.: Harmonic Analysis and the Theory of Probability, California Monogr. Math. Sci., University of California Press, Berkeley, 1955.
5. Cannarsa, P. and Vespri, V.: 'Generation of analytic semigroups by elliptic operators with unbounded coefficients', SIAM J. Math. Anal. 18 (1987), 857-872.
6. n', Israel J. Math. 61 (1988), 235-255.
7. Carasso, A.S. and Kato, T.: 'On subordinated holomorphic semigroups', Trans. Amer. Math. Soc. 327 (1991), 867-877.
8. Cerrai, S.: 'A Hille-Yosida theorem for weakly continuous semigroups', Semigroup Forum 49 (1994), 349-367.
9. n with coefficients having polynomial growth', Comm. Partial Differential Equations 21 (1996), 281-317.
10. p: Littlewood-Paley-Stein inequalities and domains of generators', J. Funct. Anal., to appear.
11. Da Prato, G. and Lunardi, A.: 'On the Ornstein-Uhlenbeck operator in spaces of continuous functions', J. Funct. Anal. 131 (1995), 94-114.
12. Ethier, S.N. and Kurtz, T.G.: Markov Processes: Characterization and Convergence, Wiley, 1986.
13. Friedman, A.: Stochastic Differential Equations and Applications, Academic Press, New York, 1975.
14. Garcia-Cuerva, J., Mauceri, G., Sjögren, P. and Torrea, J.L.: 'Higher-order Riesz operators for the Ornstein-Uhlenbeck semigroup', Potential Anal. 10 (1999), 379-407.
15. Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, 1981.
16. Jacob, N.: Pseudo Differential Operators and Markov Processes, Math. Res. 94, Akademie Verlag, Berlin, 1996.
17. Jefferies, B.: 'Weakly integrable semigroups on locally convex spaces', J. Funct. Anal. 66(3) (1986), 347-364.
18. Krylov, N.V.: Lectures on Elliptic and Parabolic Equations in Hölder Spaces, Grad. Stud. Math., Amer. Math. Soc., Providence, 1996.
19. Krylov, N.V., Röckner, M. and Zabczyk, J.: Stochastic PDE's and Kolmogorav Equations in Infinite Dimensions, Lecture Notes in Math. 1715, Springer-Verlag, 1999.
20. Lanconelli, E. and Polidoro, S.: 'On a class of hypoelliptic evolution operators', Rend. Sem. Mat. Univ. Pol. Torino 52 (1994), 26-63.
21. Lunardi, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, 1995.
22. 2 spaces with respect to invariant measures', Trans. Amer. Math. Soc. 349 (1997), 155-169.
23. Lunardi, A.: Interpolation Theory, Lectures Notes, Scuola Normale Superiore di Pisa, 1999.
24. n', Studia Math. 128(2) (1998), 171-198.
25. Marias, M.: 'Littlewood-Paley-Stein theory and Bessel diffusions', Bull. Sci. Math. (2) 111(3) (1987), 313-331.
26. Marias, M.: 'Generalised Poisson kernels and applications', Rev. Roumaine Math. Pures Appl. 35(5) (1990), 417-429.
27. p-spectrum of Ornstein-Uhlenbeck operators', Ann. Sc. Norm. Sup. Pisa 30 (2001), 97-124.
28. Ornstein, L.S. and Uhlenbeck, G.E.: Phys. Rev. 36 (1930), 823-841.
29. Priola, E.: 'On a class of Markov type semigroups in uniformly continuous and bounded functions spaces', Studia Math. 136(3) (1999), 271-295.
30. Priola, E.: 'Schauder estimates for a homogeneous Dirichlet problem in a half space of a Hilbert space', Nonlinear Anal. 44(5) (2001), 679-702.
31. Priola, E.: 'The Cauchy problem for a class of Markov type semigroups', Comm. Appl. Anal. 5(1) (2001), 49-75.
32. Priola, E.: 'On a Dirichlet problem involving an Ornstein Uhlenbeck operator', Preprint n. 26, Scuola Normale Superiore di Pisa, 2000.
33. Priola, E.: 'A counterexample to Schauder estimates for elliptic operators with unbounded coefficients', Rend. Mat. Acc. Naz. Lincei (9) 12 (2001), 15-25.
34. Schilling, R.L.: 'Subordination in the sense of Bochner and a related functional calculus', J. Austral. Math. Soc. Ser A 64(3) (1998), 368-396.
35. Stein, E.M.: Topics in Harmonic Analysis Related to the Littlewood Paley Theory, Ann. Math. Stud. 63, Princeton University Press, 1970.
36. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
37. Yosida, K.: Functional Analysis, 4th edn, Springer-Verlag, Berlin, 1974.
38. Zabczyk, J.: Mathematical Control Theory: An Introduction, Birkhäuser, 1992.