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Tr. Mat. Inst. Steklova, 2012, Volume 279, Pages 166–192 (Mi tm3431)  

This article is cited in 16 scientific papers (total in 16 papers)

Potential theory in the class of $m$-subharmonic functions

A. Sadullaeva, B. Abdullaevb

a National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan
b Urgench State University named after al-Khorezmi, Urgench, Uzbekistan

Abstract: A potential theory for the equation $(dd^\mathrm cu)^m\wedge\beta^{n-m}=f\beta^n$, $1\le m\le n$, is developed. The corresponding notions of $m$-capacity and $m$-subharmonic functions are introduced, and their properties are studied.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 279, 155–180

Bibliographic databases:

UDC: 517.55+517.57+517.957
Received in April 2012

Citation: A. Sadullaev, B. Abdullaev, “Potential theory in the class of $m$-subharmonic functions”, Analytic and geometric issues of complex analysis, Collected papers, Tr. Mat. Inst. Steklova, 279, MAIK Nauka/Interperiodica, Moscow, 2012, 166–192; Proc. Steklov Inst. Math., 279 (2012), 155–180

Citation in format AMSBIB
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\by A.~Sadullaev, B.~Abdullaev
\paper Potential theory in the class of $m$-subharmonic functions
\inbook Analytic and geometric issues of complex analysis
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 279
\pages 166--192
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3086763}
\elib{http://elibrary.ru/item.asp?id=18447448}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 279
\pages 155--180
\crossref{https://doi.org/10.1134/S0081543812080111}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314063000011}


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    This publication is cited in the following articles:
    1. Ch. H. Lu, V.-D. Nguyen, “Degenerate complex Hessian equations on compact Kahler manifolds”, Indiana Univ. Math. J., 64:6 (2015), 1721–1745  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. V. Hung, “Local property of a class of $m$-subharmonic functions”, Vietnam J. Math., 44:3 (2016), 603–621  crossref  mathscinet  zmath  isi  scopus
    3. A. Dhouib, F. Elkhadhra, “_orig m-potential theory associated to a positive closed current in the class of m-sh functions”, Complex Var. Elliptic Equ., 61:7 (2016), 875–901  crossref  mathscinet  zmath  isi  scopus
    4. M. Charabati, “Modulus of continuity of solutions to complex Hessian equations”, Int. J. Math., 27:1 (2016), 1650003  crossref  mathscinet  zmath  isi  scopus
    5. Wan D., Wang W., “Complex Hessian operator and Lelong number for unbounded $m$-subharmonic functions”, Potential Anal., 44:1 (2016), 53–69  crossref  mathscinet  zmath  isi  elib  scopus
    6. B. Abdullaev, “Nevanlinna's characteristic functions with complex Hessian potential”, Topics in Several Complex Variables, Contemporary Mathematics, 662, eds. Z. Ibragimov, N. Levenberg, S. Pinchuk, A. Sadullaev, Amer. Math. Soc., 2016, 97–105  crossref  mathscinet  zmath  isi
    7. B. I. Abdullaev, A. A. Atamuratov, M. D. Vaisova, “Analogue of the Lelong's theorem for $m$-$wsh$ functions”, Topics in Several Complex Variables, Contemporary Mathematics, 662, eds. Z. Ibragimov, N. Levenberg, S. Pinchuk, A. Sadullaev, Amer. Math. Soc., 2016, 139–144  crossref  zmath  isi
    8. H. Khedhiri, “Geometric characterization of $q$-pseudoconvex domains in $\mathbb C^n$”, Bull. Korean. Math. Soc., 54:2 (2017), 543–557  crossref  mathscinet  zmath  isi  scopus
    9. V. V. Hung, N. V. Phu, “Hessian measures on $m$-polar sets and applications to the complex Hessian equations”, Complex Var. Elliptic Equ., 62:8 (2017), 1135–1164  crossref  mathscinet  zmath  isi  scopus
    10. D. Wan, Q. Kang, “Potential theory for quatemionic plurisubharmonic functions”, Mich. Math. J., 66:1 (2017), 3–20  crossref  mathscinet  zmath  isi
    11. D. Wan, “Complex Hessian operator and generalized Lelong numbers associated to a closed $m$-positive current”, Complex Anal. Oper. Theory, 12:2 (2018), 475–489  crossref  mathscinet  zmath  isi  scopus
    12. P. Ahag, R. Czyz, L. Hed, “Extension and approximation of $m$-subharmonic functions”, Complex Var. Elliptic Equ., 63:6 (2018), 783–801  crossref  mathscinet  zmath  isi  scopus
    13. N. Q. Dieu, D. H. Hung, H. T. Anh, S. Ounheuan, “Approximation of $m$-subharmonic functions on bounded domains in $\mathbb C^n$”, J. Math. Anal. Appl., 465:2 (2018), 1039–1055  crossref  mathscinet  zmath  isi  scopus
    14. V. T. Nguyen, “A characterization of the Cegrell classes and generalized $m$-capacities”, Ann. Pol. Math., 121:1 (2018), 33–43  crossref  mathscinet  isi  scopus
    15. Ahag P., Czyz R., Hed L., “The Geometry of M-Hyperconvex Domains”, J. Geom. Anal., 28:4 (2018), 3196–3222  crossref  mathscinet  zmath  isi  scopus
    16. Elkhadhra F., “<It><Bold>M</It></Bold>-Generalized Lelong Numbers and Capacity Associated to a Class of <It><Bold>M</It></Bold>-Positive Closed Currents”, Results Math., 74:1 (2019), UNSP 10  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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