|
Integrability of superharmonic functions in a John domain
Author(s):
Hiroaki
Aikawa
Journal:
Proc. Amer. Math. Soc.
128
(2000),
195-201.
MSC (1991):
Primary 31B05
Posted:
May 27, 1999
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The integrability of positive superharmonic functions on a bounded fat John domain is established. No exterior conditions are assumed. For a general bounded John domain the  -integrability is proved with the estimate of  in terms of the John constant.
References:
- [1]
- H. Aikawa, Integrability of superharmonic functions and subharmonic functions, Proc. Amer. Math. Soc. 120 (1994), 109-117. MR 94b:31003
- [2]
- H. Aikawa, Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions, Math. Ann. 312 (1998), 289-318. CMP 99:08
- [3]
- H. Aikawa, Norm estimate for the Green operator with applications, Proceedings of Complex Analysis and Differential Equations, Marcus Wallenberg Symposium in honor of Matts Essén, Uppsala University (1997) (to appear).
- [4]
- H. Aikawa and M. Murata, Generalized Cranston-McConnell inequalities and Martin boundaries of unbounded domains, J. Analyse Math. 69 (1996), 137-152. MR 98f:31016
- [5]
- D. H. Armitage, On the global integrability of superharmonic functions in balls, J. London Math. Soc. (2) 4 (1971), 365-373.
- [6]
- D. H. Armitage, Further result on the global integrability of superharmonic functions, J. London Math. Soc. (2) 6 (1972), 109-121. MR 42:2078
- [7]
- F. W. Gehring and O. Martio, Lipschitz classes and quasiconformally homogeneous domains, Ann. Acad. Sci. Fenn. 10 (1985), 203-219. MR 87b:30029
- [8]
- Y. Gotoh, Integrability of superharmonic functions, uniform domains, and Hölder domains, Proc. Amer. Math. Soc. (to appear). CMP 98:03
- [9]
- B. Gustafsson, M. Sakai and H. S. Shapiro, On domains in which harmonic functions satisfy generalized mean value properties, Potential Analysis 7 (1997), 467-484. CMP 97:16
- [10]
- P. Lindqvist, Global integrability and degenerate quasilinear elliptic equations, J. Analyse Math. 61 (1993), 283-292. MR 95b:35062
- [11]
- F.-Y. Maeda and N. Suzuki, The integrability of superharmonic functions on Lipschitz domains, Bull. London Math. Soc. 21 (1989), 270-278. MR 90b:31004
- [12]
- M. Masumoto, A distortion theorem for conformal mappings with an application to subharmonic functions, Hiroshima Math. J. 20 (1990), 341-350. MR 91h:30031
- [13]
- M. Masumoto, Integrability of superharmonic functions on plane domains, J. London Math. Soc. (2) 45 (1992), 62-78. MR 93f:31002
- [14]
- W. Smith and D. A. Stegenga, Hölder domains and Poincaré domains, Trans. Amer. Math. Soc. 319 (1990), 67-100. MR 90i:30012
- [15]
- W. Smith and D. A. Stegenga, Exponential integrability of the quasi-hyperbolic metric on Hölder domains, Ann. Acad. Sci. Fenn. 16 (1991), 345-360. MR 93b:30016
- [16]
- D. A. Stegenga and D. C. Ullrich, Superharmonic functions in Hölder domains, Rocky Mountain J. Math. 25 (1995), 1539-1556. MR 97j:31003
- [17]
- W. P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, 1989. MR 91e:46046
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
31B05
Retrieve articles in all Journals with MSC
(1991):
31B05
Additional Information:
Hiroaki
Aikawa
Affiliation:
Department of Mathematics, Shimane University, Matsue 690-8504, Japan
Email:
haikawa@math.shimane-u.ac.jp
DOI:
10.1090/S0002-9939-99-04991-6
PII:
S 0002-9939(99)04991-6
Received by editor(s):
March 17, 1998
Posted:
May 27, 1999
Additional Notes:
This work was supported in part by Grant-in-Aid for Scientific Research (B) (No. 09440062), Japanese Ministry of Education, Science and Culture.
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org