Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao

Studia Mathematica (1994)

  • Volume: 108, Issue: 1, page 25-48
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Zhao, Shiying. "Boundary behavior of subharmonic functions in nontangential accessible domains." Studia Mathematica 108.1 (1994): 25-48. <http://eudml.org/doc/216038>.

@article{Zhao1994,
abstract = {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.},
author = {Zhao, Shiying},
journal = {Studia Mathematica},
keywords = {subharmonic function; Green potential; boundary limit; NTA domain; subharmonic functions; nontangential accessible domains in the sense of Jerison and Kenig; Green potentials},
language = {eng},
number = {1},
pages = {25-48},
title = {Boundary behavior of subharmonic functions in nontangential accessible domains},
url = {http://eudml.org/doc/216038},
volume = {108},
year = {1994},
}

TY - JOUR
AU - Zhao, Shiying
TI - Boundary behavior of subharmonic functions in nontangential accessible domains
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 1
SP - 25
EP - 48
AB - 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.
LA - eng
KW - subharmonic function; Green potential; boundary limit; NTA domain; subharmonic functions; nontangential accessible domains in the sense of Jerison and Kenig; Green potentials
UR - http://eudml.org/doc/216038
ER -

References

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  1. [1] L. Carleson, On the existence of boundary values for harmonic functions in several variables, Ark. Mat. 4 (1962), 393-399. Zbl0107.08402
  2. [2] B. E. J. Dahlberg, On estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 272-288. Zbl0406.28009
  3. [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. Zbl0402.31011
  4. [4] J. L. Doob, Classical Potential Theory and Its Probabilistic Counterpart, Springer, New York, 1984. 
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  6. [6] L. L. Helms, Introduction of Potential Theory, Wiley-Interscience, New York, 1969. Zbl0188.17203
  7. [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. Zbl0514.31003
  8. [8] D. S. Jerison and C. E. Kenig, Hardy spaces, A ∞ , and singular integrals on chord-arc domains, Math. Scand. 50 (1982), 221-247. Zbl0509.30025
  9. [9] J. E. Littlewood, On functions subharmonic in a circle (II), Proc. London Math. Soc. (2) 28 (1928), 383-394. Zbl54.0516.04
  10. [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. [11] E. M. Stein, On the theory of harmonic functions of several variables. II. Behavior near the boundary, Acta Math. 106 (1961), 137-174. Zbl0111.08001
  12. [12] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
  13. [13] J. C. Taylor, Fine and nontangential convergence on an NTA domain, Proc. Amer. Math. Soc. 91 (1984), 237-244. Zbl0542.31004
  14. [14] D. Ullrich, Radial limits of M-subharmonic functions, Trans. Amer. Math. Soc. 292 (1985), 501-518. Zbl0609.31003
  15. [15] K.-O. Widman, On the boundary behavior of solutions to a class of elliptic partial differential equations, Ark. Mat. 6 (1967), 485-533. Zbl0166.37702
  16. [16] R. Wittmann, Positive harmonic functions on nontangentially accessible domains, Math. Z. 190 (1985), 419-438. Zbl0555.31006
  17. [17] J.-M. Wu, L p -densities and boundary behavior of Green potentials, Indiana Univ. Math. J. 28 (1979), 895-911. Zbl0449.31003
  18. [18] L. Ziomek, On the boundary behavior in the metric L p of subharmonic functions, Studia Math. 29 (1967), 97-105. Zbl0157.42604

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