Abstract
We prove classical inequalities for generalized second-order differential operators in order to study some potential theoretic properties of convex functions and associated diffusions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BEDFORD, E. and M. KALKA: ‘Foliations and complex Monge-Ampere equations’, Comm. Pure Appl. Math. 30 (1977), 543–570.
BEDFORD, E. and B.A. TAYLOR: ‘Variational properties of the complex Monge-Ampère equation II. Intrinsic norm’, Amer, J. Math. 101 (1979), 1131–1166.
CEGRELL, U.: ‘On the domains of existence for plurisubharmonic functions’, Banach Center Publications 11 (1983), 33–37.
DYNKIN, E.B.: Markov processes, vols. 1, 2, Springer-Verlag, Berlin 1965.
FUKUSHIMA, M.: Dirichlet forms and Markov processes, Kodansha and North-Holland, 1980.
FUKUSHIMA, M. and M. OKADA: ‘On conformai martingale diffusions and pluripolar sets’, J. Functional Anal. 55 (1984), 377–388.
GAVEAU, B. and J. ŁAWRYNOWICZ: ‘Intégrale de Dirichlet sur une variété complexe I’, in: Lect. Notes in Math. 919, Springer 1982, pp. 131–167.
KALINA, J. and J. ŁAWRYNOWICZ: ‘Foliations and the generalized complex Monge-Ampère equations’, Banach Center Publications 11 (1983), 111–119.
ŁAWRYNOWICZ, J. and M. OKADA: ‘Canonical diffusion and foliation involving the complex hessian’, Bull. Polish Acad. Sei. Math. 34 (1986), 661–667.
OKADA, M.: ‘Espaces de Dirichlet généraux en analyse complexe’, J. Functional Anal. 46 (1982), 396–410.
OKADA, M.: ‘Sur une capacité définie par la forme de Dirichlet associée aux fonctions plurisousharmoniques’, Tôhoku Math. J. 35 (1983), 513–517.
RAUCH, J. and B.A. TAYLOR: ‘The Dirichlet problem for the multidimensional Monge-Ampère equation’, Rocky Mountain J. Math. 7 (1977), 345–364.
SICIAK, J.: ‘Extremal plurisubharmonic functions and capacities in ℂn, Lect. Notes Sophia Univ. 14 (1982).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Okada, M. (1989). Symbolic Calculus Applied to Convex Functions and Associated Diffusions. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_29
Download citation
DOI: https://doi.org/10.1007/978-94-009-2643-1_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7693-7
Online ISBN: 978-94-009-2643-1
eBook Packages: Springer Book Archive