Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-13T22:47:37.145Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergence in Capacity

Published online by Cambridge University Press:  20 November 2018

Urban Cegrell
Urban Cegrell*
Affiliation:
Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 UmeÅ, Sweden e-mail: Urban.Cegrell@math.umu.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this note we study the convergence of sequences of Monge–Ampère measures $\{{{(d{{d}^{c}}{{u}_{s}})}^{n}}\}$ , where $\{{{u}_{s}}\}$ is a given sequence of plurisubharmonic functions, converging in capacity.

Keywords

32U2031C15complex Monge–Ampère operatorconvergence in capacityplurisubharmonic function

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012, pp. 242 - 248
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Åhag, P. and Czyż, R., On the Cegrell classes. Math. Z. 256(2007), no. 2, 243–264. http://dx.doi.org/10.1007/s00209-006-0067-2 Google Scholar
[2] Bloom, T. and Levenberg, N., Capacity convergence results and applications to a Bernstein-Markov inequality. Trans. Amer. Math. Soc. 351(1999), no. 12, 4753–4767. http://dx.doi.org/10.1090/S0002-9947-99-02556-8 Google Scholar
[3] Cegrell, U., Discontinuité de l’opératur de Monge-Ampère complexe. C. R.Acad.Sci. Paris Sér. I Math. 296(1983), no. 21, 869–871.Google Scholar
[4] Cegrell, U., Pluricomplex energy. Acta Math. 180(1998), no. 2, 187–217. http://dx.doi.org/10.1007/BF02392899 Google Scholar
[5] Cegrell, U., Convergence in capacity. Isaac Newton Institute for Mathematical Sciences preprint series NI01046-NPD (2001). arxiv:math/0505218v1Google Scholar
[6] Cegrell, U., The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier (Grenoble) 54(2004), no. 1, 159–179.Google Scholar
[7] Cegrell, U., Weak*-convergence of Monge-Ampère measures. Math. Z. 254(2006), no. 3, 505–508. http://dx.doi.org/10.1007/s00209-006-0953-7 Google Scholar
[8] Cegrell, U., Approximation of plurisubharmonic functions in hyperconvex domains. In: Complex Analysis and Digital Geometry. Acta Universitatis Upsaliensis Skr. Uppsala Univ. C. Organ. Hist.86. Uppsala Universitet, Uppsala, 2009 pp. 125–129.Google Scholar
[9] Kolodziej, S., The complex Monge-Ampère equation and pluripotential theory. Mem. Amer. Math. Soc. 178(2005), no. 840.Google Scholar
[10] Nguyễn, V. K. and Pham, A., A. comparison principle for the complex Monge-Ampère operator in Cegrell's classes and applications. Trans. Amer. Math. Soc. 361(2009), no. 10, 5539–5554. http://dx.doi.org/10.1090/S0002-9947-09-04730-8 Google Scholar
[11] Xing, Y., A decomposition of Monge-Ampère measures. Ann. Polon. Math. 92(2007), no. 2, 191–195. http://dx.doi.org/10.4064/ap92-2-7 Google Scholar
[12] Xing, Y., Continuity of the complex Monge-Ampère operator. Proc. Amer. Math. Soc. 124(1996), no. 2, 457–467. http://dx.doi.org/10.1090/S0002-9939-96-03316-3 Google Scholar
[13] Xing, Y., Weak convergence of current. Math. Z. 260(2008), no. 2, 253–264. http://dx.doi.org/10.1007/s00209-007-0271-8 Google Scholar
[14] Xing, Y., Convergence in capacity. Ann. Inst. Fourier (Grenoble) 58(2008), no. 5, 1839–1861.Google Scholar