Skip to main content

Two topics related to Dirichlet forms: quasi everywhere convergences and additive functionals

  • Chapter
  • First Online:
Dirichlet Forms

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1563))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References in §1

  1. D.R. Adams, Maximal operators and capacity, Proc. Amer. Math. Soc. 34(1972),152–156.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Albeverio and M. Röckner, Dirichlet forms on topological vector spaces—the construction of the associated diffusion process, Probab. Th. Rel. Fields 83(1989),405–434.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Albeverio and Z.M. Ma, A note on quasi continuous kernels representing quasi linear maps, Forum Math., 3(1991),389–400.

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Albeverio, M. Fukushima, W. Hansen, Z.M. Ma and M. Röckner, Capacities on Wiener space: tihgtness and invariance, C.R. Acad. Sci. Paris, 312(1991),931–935.

    MATH  Google Scholar 

  5. J.A. Clarkson, uniform convex spaces, TAMS, 40(1936),396–414.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Fukushima, Dirichlet forms and Markov processes, Kodansha and North-Holland, 1980.

    Google Scholar 

  7. M. Fukushima, Capacitary maximal inequalities and an ergodic theorem, in “Probability Thoery and Mathematical Statistics” eds. K. Ito and I.V. Prokhorov, LNM 1021 Springer, 1983

    Google Scholar 

  8. M. Fukushima, (r,p)-capacities and Hunt processes in infinite dimensions, in Proceedings of 6-th Japan Soviet Symp. at Kiev, 1991, World Scientific, Singapore, to appear

    Google Scholar 

  9. M. Fukushima and H. Kaneko, On (r,p)-capacities for general Markovian semigroups, in “Infinite dimensional analysis and stochastic processes”, ed. S. Albeverio, Pitman, 1985

    Google Scholar 

  10. M. Fukushima, N. Jacob and H. Kaneko, On (r,2)-capacities for a class of elliptic pseudo differential operators, Math. Ann. 293(1992),343–348

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Kaneko, On (r,p)-capacities for Markov processes, Osaka J. Math., 23(1986),325–336.

    MathSciNet  MATH  Google Scholar 

  12. T. Kazumi and I. Shigekawa, Measures of finite (r,p)-evergy and potentials on a separable metric space, Preprint

    Google Scholar 

  13. E.M. Stein, Topics in harmonic analysis, Annals Math. Studies 63, Princeton Univ. Press, 1970. *** DIRECT SUPPORT *** A00I6B21 00002

    Google Scholar 

References in §2

  1. R. Baňuelos and B. Oksendal, A stochastic approach to quasi everywhere boundary convergence of harmonic functions, J. Funct. Anal. 72(1987),13–27

    Article  MathSciNet  MATH  Google Scholar 

  2. N.K. Bary, A treatise on trigonometric series, Pergammon, Oxford, 1964

    MATH  Google Scholar 

  3. A. Beurling, Ensembles exceptinelles, Acta Math. 72(1940),1–13

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Carleson, Selected problem on exceptional sets. Van Nostrand, Princeton, 1967

    MATH  Google Scholar 

  5. Ana Bela Cruzeiro, Convergence quasi partout dans des domains paraboliques des fonctions d'intégrale de Dirichlet finie, C.R.A.S. Paris, t. 294(1982),13–16

    MathSciNet  MATH  Google Scholar 

  6. Ana Bela Cruzeiro, Convergence au bord pour les fonctions harmoniques dans R d de la class de Sobolev W d1 , C.R.A.S. Paris, t294 (1982),71–74

    MathSciNet  MATH  Google Scholar 

  7. J. Deny, Méthods Hilbertiennes et theorie du potentiel, Potential Theory, CIME, Edizioni Cremonese, Roma, 1970

    MATH  Google Scholar 

  8. R. Durrett, Brownian motion and martingales in analysis, Wadsworth, Belmond, Calif. 1984

    MATH  Google Scholar 

  9. M. Fukushima, Dirichlet forms and Markov processes, Kodansha and North Holland, 1980

    Google Scholar 

  10. M. Fukushima, Capacitary maximal inequalities and an ergodic theorem, in “Probability theory and Mathematical statistics”, eds. K. Ito and J. V. Prohorov, LNM 1021, Springer, 1983

    Google Scholar 

  11. O.G. Jorsboe and L. Mejlbro, The Carleson-Hunt theorem on Fourier series, LNM 911, Springer, 1982

    Google Scholar 

  12. R.A. Hunt, On the convergence of Fourier series, in Proc. S.I.U. Conf. on Orthogonal expansions, Southern Illinois Univ. Press, Carbondale, 1968

    Google Scholar 

  13. C.J. Preston, A theory of capacities and its application to some convergence results, Adv. Math. 6(1971),78–106

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Nagel, W. Rudin and J.H. Shapiro, Tangential boundary behavior of function in Dirichlet-type spaces, Ann. Math. 116(1982),331–360

    Article  MathSciNet  MATH  Google Scholar 

  15. E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970

    Google Scholar 

  16. A. Zygmund, Trigonometric series, Cambridge Univ. Press, 1968

    Google Scholar 

References in §3

  1. N. Bouleau and F. Hirsch, Dirichlet forms and analysis on Wiener space, Walter de Gruyter, 1991

    Google Scholar 

  2. C. Dellacherie and P. Meyer, Probability and potential B, North-Holland, 1982

    Google Scholar 

  3. M. Fukushima, Capacitary maximal inequalities and an ergodic theorem, in “Probability Theory and Mathematical Statistics”, eds. K. Ito and J.V. Prohorov, LNM 911, Springer, 1982

    Google Scholar 

  4. H. Kaneko, On (r, p)-capacities for Markov processes, Osaka J. Math., 23(1986),325–336

    MathSciNet  MATH  Google Scholar 

  5. S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Tata Institute of Fundamental Research, vol. 73, Springer-Verlag, 1984

    Google Scholar 

References in §4

  1. J. Baxter, G. Dal Maso and U. Mosco, Stopping times and Γ-convergence, TAMS 303(1987),1–38

    MathSciNet  MATH  Google Scholar 

  2. R.M. Blumenthal and R.K. Getoor, Markov processes and potential theory, Academic press, 1968

    Google Scholar 

  3. E.B. Dynkin, Markov processes, Springer, 1965

    Google Scholar 

  4. M. Fukushima, Dirichlet forms and Markov processes, Kodansha and North-Holland, 1980

    Google Scholar 

  5. M. Fukushima, On two classes of smooth measures for symmetric Markov processes, in “Stochastic Analysis”, eds. M. Metivier and S. Watanabe, Lecture Notes in Math. 1322, Springer, 1988

    Google Scholar 

  6. R.K. Getoor and M.J. Sharpe, Naturality, standardness and weak duality for Markov processes, Z. Wahrscheinlichleitsthoerie verw. Gebiete, 67(1984),1–62

    Article  MathSciNet  MATH  Google Scholar 

  7. H.P. McKean and H. Tanaka, Additive functionals of the Brownian path, Memoire Coll. Sci. Univ. Kyoto 33(1961),479–506

    MathSciNet  MATH  Google Scholar 

  8. D. Revuz, Mésures associées aux fonctionelles additives de Markov I, TAMS 148(1970), 501–531

    MathSciNet  MATH  Google Scholar 

  9. M.L. Silverstein, Symmetric Markov processes, Lecture Notes in Math. 426, Springer, 1974

    Google Scholar 

  10. K.-T. Sturm, Measures charging no polar sets and additive functionals of Brownian motion, Forum Math. 4(1992),257–297

    Article  MathSciNet  MATH  Google Scholar 

  11. K-T. Sturm, Schrödinger operators and Feynman-Kac semigroups with arbitrary nonnegative potentials, in “Operator Calculus and Spectral Theory”, eds. Demuth and Schulze, Birkhäuser, to appear

    Google Scholar 

  12. A.D. Wenzell, Nonnegative additive functionals of Markov processes, DAH 137(1961), 17–20

    Google Scholar 

References in §5

  1. R.F. Bass and Pei Hsu, The seminartingale structure of reflecting Brownian motion, Proc. AMS 108(1990),1007–1010

    Article  MathSciNet  MATH  Google Scholar 

  2. R.F. Bass and Pei Hsu, Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, Ann. Prob. 19(1991),486–508

    Article  MathSciNet  MATH  Google Scholar 

  3. Z.Q. Chen, P.J. Fitzsimmons and R.J. Williams, Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets, Preprint

    Google Scholar 

  4. M. Fukushima, A construction of reflecting barrier Brownian motions for bounded domains, Osaka J. Math. 4(1967),183–215

    MathSciNet  MATH  Google Scholar 

  5. M. Fukushima, Dirichlet forms and Markov processes, Kodansha, North Holland 1980

    MATH  Google Scholar 

  6. H. Tanaka, Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J. 9(1979),163–177 *** DIRECT SUPPORT *** A00I6B21 00003

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gianfausto Dell'Antonio Umberto Mosco

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this chapter

Cite this chapter

Fukushima, M. (1993). Two topics related to Dirichlet forms: quasi everywhere convergences and additive functionals. In: Dell'Antonio, G., Mosco, U. (eds) Dirichlet Forms. Lecture Notes in Mathematics, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074090

Download citation

  • DOI: https://doi.org/10.1007/BFb0074090

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57421-7

  • Online ISBN: 978-3-540-48151-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics