Article PDF
Avoid common mistakes on your manuscript.
References
Adams, D. R. andMeyers, N. G., Bessel potentials. Inclusion relations among classes of exceptional sets.Indiana Univ. Math. J. 22 (1973), 873–905.
Ahlfors, L.,Conformal invariants: Topics in geometric function theory. Mc Graw-Hill 1973.
——»- andBeurling, A., conformal invariants and function-theoretic null-sets.Acta Math. 83 (1950), 101–129.
Bagby, T., Quasi topologies and rational approximation.J. Functional Analysis 10 (1972), 259–268.
Bardet, J.-P. andLelong-Ferrand, J., Relation entre le q-module et la p-capacité d’un condensateur Riemannien,C. R. Acad. Sci Paris 277 (1973), 835–838.
Carleson, L.,Selected problems on exceptional sets, Van Nostrand, Princeton, N. J. (1967).
Deny, J. andLions, J. L., Les espaces du type de Beppo Levi.Ann. Inst. Fourier (Grenoble) 5 (1953–1954), 305–370.
Fuglede, B., Extremal length and functional completion.Acta Math. 98 (1957), 171–219.
Gehring, F. W., Extremal length definitions for the conformal capacity of rings in space,Michigan Math. J. 9 (1962), 137–150.
Gončar, A. A., On the property of instability of harmonic capacity.Dokl. Akad. Nauk SSSR 165 (1965), 479–481.(Soviet Math. Dokl.) 6 (1965), 1458–1460.)
Harvey, R. andPolking, J. C., A notion of capacity which characterizes removable singularities.Trans. Amer. Math. Soc., 169 (1972) 183–195.
Hedberg, L. I., The Stone-Weierstrass theorem in certain Banach algebras of Fourier type.Ark. mat. 6 (1965), 77–102.
——»-, The Stone-Weierstrass theorem in Lipschitz algebras.Ark. mat. 8 (1969), 63–72.
——»-, Approximation in the mean by analytic functions,Trans. Amer. Math. Soc. 163 (1972), 157–171.
——»-, Non-linear potentials and approximation in the mean by analytic functions.Math. Z. 129 (1972), 299–319.
Hesse, J., Ap-extremal length andp-capacity equality, to appear.
Lelong-Ferrand, J., Étude d’une classe d’applications liées à des homomorphismes d’algèbres de fonctions, et généralisant les quasi conformes.Duke Math. J. 40 (1973). 163–186.
Lewis, L. G., Quasiconformal mappings and Royden algebras in space.Trans. Amer. Math. Soc. 158 (1971), 481–492.
Marden, A. andRodin, B., Extremal and conjugate extremal distance on open Riemann surfaces with applications to circular radial slit mappings.Acta Math. 115 (1966), 237–269.
Maz’ja, V. G., On the continuity at a boundary point of the solution of quasi-linear elliptic equations (Russian.)Vestnik Leningrad. Univ. 25 no. 13 (1970), 42–55.
——»- andHavin, V. P., Non-linear potential theory. (Russian.)Uspehi Mat. Nauk 26 no. 6 (1972), 67–138.
Meyers, N. G., A theory of capacities for potentials of functions in Lebesgue classes.Math. Scand. 26 (1970), 255–292.
Ohtsuka, M., Extremal length and precise functions in 3-space.Lecture notes, Hiroshima University (1973).
Polking, J. C., Approximation inLp by solutions of elliptic partial differential equations.American J. Math. 94 (1972), 1231–1244.
Rodin, B. andSario, L.,Principal functions, Van Nostrand, Princeton, N. J., (1968).
Royden, H. L., On a class of null-bounded Riemann surfaces.Comment. Math. Helv. 34 (1960), 52–66.
Sario, L. andNakai, M.,Classification theory of Riemann surfaces, Springer-Verlag, Berlin-Heidelberg-New York (1970).
Stein, E. M.,Singular integrals and differentiability properties of functions, Princeton Univ. Press (1970).
Väisälä, J., On the null-sets for extremal distances.Ann. Acad. Sci. Fenn. Ser. A. I. 322 (1962), 1–12.
Vituškin, A. G., Analytic capacity of sets in problems of approximation theory.Uspehi Mat. Nauk. 22 no. 6 (1967), 141–199(Russian Math. Surveys 22 (1967), 139–200.)
Yamamoto, H., On KD-null sets in N-dimensional Fuclidean space,J. Sci Hiroshima Univ. Ser. A-I 34 (1970), 59–68.
Ziemer, W. P., Extremal length and conformal capacity.Trans. Amer. Math. Soc. 126 (1967), 460–473.
——→-, Extremal length and p-capacity,Michigan Math. J. 16 (1969), 43–51.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hedberg, L.I. Removable singularities and condenser capacities. Ark. Mat. 12, 181–201 (1974). https://doi.org/10.1007/BF02384755
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384755