Fine and nontangential convergence on an NTA domain
Author:
J. C. Taylor
Journal:
Proc. Amer. Math. Soc. 91 (1984), 237-244
MSC:
Primary 31B25; Secondary 31A20
DOI:
https://doi.org/10.1090/S0002-9939-1984-0740178-4
MathSciNet review:
740178
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Abstract | References | Similar Articles | Additional Information
Abstract: The recent article by Jerison and Kenig on "Boundary behaviour of harmonic functions in nontangentially accessible domains" did not consider the relation between fine limits and nontangential limits. The results in this direction obtained by Hunt & Wheeden [5] for Lipschitz domains are extended here to NTA domains.
- [1] M. Brelot and J. L. Doob, Limites angulaires et limites fines, Ann. Inst. Fourier (Grenoble) 13 (1963), no. fasc., fasc. 2, 395–415 (French). MR 196107
- [2] J. L. Doob, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. France 85 (1957), 431–458. MR 109961
- [3] Kohur Gowrisankaran, Extreme harmonic functions and boundary value problems. II, Math. Z. 94 (1966), 256–270. MR 201660, https://doi.org/10.1007/BF01111455
- [4] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. MR 0261018
- [5] Richard A. Hunt and Richard L. Wheeden, Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc. 147 (1970), 507–527. MR 274787, https://doi.org/10.1090/S0002-9947-1970-0274787-0
- [6] Peter W. Jones, A geometric localization theorem, Adv. in Math. 46 (1982), no. 1, 71–79. MR 676987, https://doi.org/10.1016/0001-8708(82)90054-8
- [7] Peter W. Jones, A geometric localization theorem, Adv. in Math. 46 (1982), no. 1, 71–79. MR 676987, https://doi.org/10.1016/0001-8708(82)90054-8
- [8] Adam Korányi and J. C. Taylor, Fine convergence and admissible convergence for symmetric spaces of rank one, Trans. Amer. Math. Soc. 263 (1981), no. 1, 169–181. MR 590418, https://doi.org/10.1090/S0002-9947-1981-0590418-1
- [9] Linda Naïm, Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier, Grenoble 7 (1957), 183–281 (French). MR 0100174
- [10] J. C. Taylor, An elementary proof of the theorem of Fatou-Naïm-Doob, 1980 Seminar on Harmonic Analysis (Montreal, Que., 1980) CMS Conf. Proc., vol. 1, Amer. Math. Soc., Providence, R.I., 1981, pp. 153–163. MR 670103
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0740178-4
Keywords:
Fine convergence,
NTA-domain
Article copyright:
© Copyright 1984
American Mathematical Society