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1994 | 108 | 1 | 25-48
Tytuł artykułu

Boundary behavior of subharmonic functions in nontangential accessible domains

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The following results concerning boundary behavior of subharmonic functions in the unit ball of $ℝ^n$ are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek's theorem on the $L^p$-nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
108
Numer
1
Strony
25-48
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-06-30
Twórcy
autor
  • Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121, U.S.A.
Bibliografia
  • [1] L. Carleson, On the existence of boundary values for harmonic functions in several variables, Ark. Mat. 4 (1962), 393-399.
  • [2] B. E. J. Dahlberg, On estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 272-288.
  • [3] B. E. J. Dahlberg, On the existence of radial boundary values for functions subharmonic in a Lipschitz domain, Indiana Univ. Math. J. 27 (1978), 515-526.
  • [4] J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart, Springer, New York, 1984.
  • [5] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969.
  • [6] L. L. Helms, Introduction of Potential Theory, Wiley-Interscience, New York, 1969.
  • [7] D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. in Math. 46 (1982), 80-147.
  • [8] D. S. Jerison and C. E. Kenig, Hardy spaces, $A_∞$, and singular integrals on chord-arc domains, Math. Scand. 50 (1982), 221-247.
  • [9] J. E. Littlewood, On functions subharmonic in a circle (II), Proc. London Math. Soc. (2) 28 (1928), 383-394.
  • [10] L. Naïm, Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier (Grenoble) 7 (1957), 183-281.
  • [11] E. M. Stein, On the theory of harmonic functions of several variables. II. Behavior near the boundary, Acta Math. 106 (1961), 137-174.
  • [12] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
  • [13] J. C. Taylor, Fine and nontangential convergence on an NTA domain, Proc. Amer. Math. Soc. 91 (1984), 237-244.
  • [14] D. Ullrich, Radial limits of M-subharmonic functions, Trans. Amer. Math. Soc. 292 (1985), 501-518.
  • [15] K.-O. Widman, On the boundary behavior of solutions to a class of elliptic partial differential equations, Ark. Mat. 6 (1967), 485-533.
  • [16] R. Wittmann, Positive harmonic functions on nontangentially accessible domains, Math. Z. 190 (1985), 419-438.
  • [17] J.-M. Wu, $L^p$-densities and boundary behavior of Green potentials, Indiana Univ. Math. J. 28 (1979), 895-911.
  • [18] L. Ziomek, On the boundary behavior in the metric $L^p$ of subharmonic functions, Studia Math. 29 (1967), 97-105.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv108i1p25bwm
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