Integrability of superharmonic functions, uniform domains, and Hölder domains
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- by Yasuhiro Gotoh
- Proc. Amer. Math. Soc. 127 (1999), 1443-1451
- DOI: https://doi.org/10.1090/S0002-9939-99-04670-5
- Published electronically: January 29, 1999
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Abstract:
Let $S^+(D)$ denote the space of all positive superharmonic functions on a domain $D \subset \mathbf R^n$. Lindqvist showed that $\log S^+(D)$ is a bounded subset of $BMO(D)$. Using this, we give a characterization of finitely connected $2$-dimensional uniform domains and remarks on Hölder domains.References
- Hiroaki Aikawa, Integrability of superharmonic functions and subharmonic functions, Proc. Amer. Math. Soc. 120 (1994), no. 1, 109–117. MR 1169019, DOI 10.1090/S0002-9939-1994-1169019-7
- F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50–74 (1980). MR 581801, DOI 10.1007/BF02798768
- Y. Gotoh, On global integrability of $BMO$ functions on general domains, to appear in J. Anal. Math.
- Peter Lindqvist, Global integrability and degenerate quasilinear elliptic equations, J. Anal. Math. 61 (1993), 283–292. MR 1253445, DOI 10.1007/BF02788845
- Fumi-Yuki Maeda and Noriaki Suzuki, The integrability of superharmonic functions on Lipschitz domains, Bull. London Math. Soc. 21 (1989), no. 3, 270–278. MR 986371, DOI 10.1112/blms/21.3.270
- Makoto Masumoto, Integrability of superharmonic functions on plane domains, J. London Math. Soc. (2) 45 (1992), no. 1, 62–78. MR 1157552, DOI 10.1112/jlms/s2-45.1.62
- Makoto Masumoto, Integrability of superharmonic functions on Hölder domains of the plane, Proc. Amer. Math. Soc. 117 (1993), no. 4, 1083–1088. MR 1152284, DOI 10.1090/S0002-9939-1993-1152284-9
- Hans Martin Reimann and Thomas Rychener, Funktionen beschränkter mittlerer Oszillation, Lecture Notes in Mathematics, Vol. 487, Springer-Verlag, Berlin-New York, 1975 (German). MR 0511997, DOI 10.1007/BFb0081825
- Wayne Smith and David A. Stegenga, Exponential integrability of the quasi-hyperbolic metric on Hölder domains, Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), no. 2, 345–360. MR 1139802, DOI 10.5186/aasfm.1991.1625
- Wayne Smith and David A. Stegenga, Sobolev imbeddings and integrability of harmonic functions on Hölder domains, Potential theory (Nagoya, 1990) de Gruyter, Berlin, 1992, pp. 303–313. MR 1167248
- David A. Stegenga and David C. Ullrich, Superharmonic functions in Hölder domains, Rocky Mountain J. Math. 25 (1995), no. 4, 1539–1556. MR 1371353, DOI 10.1216/rmjm/1181072160
- Noriaki Suzuki, Note on the integrability of superharmonic functions, Proc. Amer. Math. Soc. 118 (1993), no. 2, 415–417. MR 1126201, DOI 10.1090/S0002-9939-1993-1126201-1
Bibliographic Information
- Yasuhiro Gotoh
- Email: gotoh@cc.nda.ac.jp
- Received by editor(s): May 7, 1997
- Received by editor(s) in revised form: August 25, 1997
- Published electronically: January 29, 1999
- Communicated by: Albert Baernstein II
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1443-1451
- MSC (1991): Primary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-99-04670-5
- MathSciNet review: 1476132