Hedberg, L. I.; Wolff, Th. H. Thin sets in nonlinear potential theory. (English) Zbl 0508.31008 Ann. Inst. Fourier 33, No. 4, 161-187 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 137 Documents MSC: 31B99 Higher-dimensional potential theory 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 31B15 Potentials and capacities, extremal length and related notions in higher dimensions Keywords:thin sets; Kellogg and Choquet properties; Wiener criterion; nonlinear potentials × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [1] and , Inclusion relations among fine topologies in non-linear potential theory, Indiana Univ. Math. J., to appear. · Zbl 0545.31011 [2] [2] and , Thinness and Wiener criteria for non-linear potentials, Indiana Univ. Math. J., 22 (1972), 169-197. · Zbl 0244.31012 [3] [3] , Quasi topologies and rational approximation, J. Funct. Anal., 10 (1972), 259-268. · Zbl 0266.30024 [4] [4] , A general form of the covering principle and relative differentiation of additive functions I, II. Proc. Cambridge Philos. Soc., 41 (1945), 103-110, ibid., 42 (1946), 1-10. · Zbl 0063.00353 [5] [5] , Sur les ensembles effilés, Bull. Sci. Math., 68 (1944), 12-36. · Zbl 0028.36201 [6] [6] , On topologies and boundaries in potential theory, Lecture Notes in Math., 175, Springer Verlag 1971. · Zbl 0222.31014 [7] [7] , Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math., 4 (1961), 33-49. · Zbl 0195.41103 [8] [8] , Selected problems on exceptional sets, Van Nostrand, 1967. · Zbl 0189.10903 [9] [9] , Sur les points d’effilement d’un ensemble. Application à l’étude de la capacité, Ann. Inst. Fourier, Grenoble, 9 (1959), 91-101. · Zbl 0093.29702 [10] [10] , Convergence vague et suites de potentiels newtoniens, Bull. Sci. Math., 99 (1975), 157-164. · Zbl 0313.31020 [11] [11] , Uniformly convex spaces, Trans. Amer. Math. Soc., 40 (1936), 396-414. · JFM 62.0460.04 [12] [12] , Les points irréguliers dans la théorie du potentiel et le critère de Wiener, Kungl. Fysiogr. Sällsk. i Lund Förh., 9-2 (1939), 1-10. · JFM 65.0415.05 [13] [13] , Quasi topology and fine topology, Séminaire de Théorie du Potentiel, 10 (1965-1966), no. 12. · Zbl 0164.14002 [14] [14] , The quasi topology associated with a countably additive set function, Ann. Inst. Fourier, Grenoble, 21-1 (1971), 123-169. · Zbl 0197.19401 [15] [15] , Imbedding theorems of Sobolev type in potential theory, Math. Scand., 45 (1979), 77-102. · Zbl 0437.31009 [16] [16] , Approximation in the mean by analytic functions, Dokl. Akad. Nauk SSSR, 178 (1968), 1025-1028. · Zbl 0182.40201 [17] [17] , Non-linear potentials and approximation in the mean by analytic functions, Math. Z., 129 (1972), 299-319. · Zbl 0236.31010 [18] [18] , Two approximation problems in function spaces, Ark. Mat., 16 (1978), 51-81. · Zbl 0399.46023 [19] [19] , Spectral synthesis and stability in Sobolev spaces, in Euclidean harmonic analysis (Proc., Univ. of Maryland, 1979), Lecture Notes in Math., 779, 73-103, Springer Verlag 1980. · Zbl 0469.31003 [20] [20] , Spectral synthesis in Sobolev spaces, and uniqueness of solutions of the Dirichlet problem, Acta Math., 147 (1981), 237-264. · Zbl 0504.35018 [21] [21] , On the Dirichlet problem for higher order equations, in Conference on Harmonic Analysis in Honor of Antoni Zygmund (Chicago 1981), 620-633. Wadsworth, 1983. · Zbl 0532.35026 [22] [22] , A uniqueness theorem for higher order elliptic partial differential equations, Math. Scand., 51 (1982), 323-332. · Zbl 0491.35045 [23] [23] , Foundations of modern potential theory, Nauka, Moscow 1966. (English translation, Springer-Verlag 1972). · Zbl 0253.31001 [24] [24] and , Non-linear potential theory, Uspehi Mat. Nauk, 27-6 (1972), 67-138. · Zbl 0247.31010 [25] [25] , Continuity properties of potentials, Duke Math. J., 42 (1975), 157-166. · Zbl 0334.31004 [26] [26] , Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970. · Zbl 0207.13501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.