Arkiv för Matematik

  • Ark. Mat.
  • Volume 16, Number 1-2 (1978), 51-81.

Two approximation problems in function spaces

Lars Inge Hedberg

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Note

The author gratefully acknowledges partial support from the Swedish Natural Science Research Council (NFR) under contract nr F 2234-012, and from the Centre National de la Recherche Scientifique under the ATP franco-suédoise.

Article information

Source
Ark. Mat., Volume 16, Number 1-2 (1978), 51-81.

Dates
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896544

Digital Object Identifier
doi:10.1007/BF02385982

Mathematical Reviews number (MathSciNet)
MR499137

Zentralblatt MATH identifier
0399.46023

Rights
1978 © Institut Mittag-Leffler

Citation

Hedberg, Lars Inge. Two approximation problems in function spaces. Ark. Mat. 16 (1978), no. 1-2, 51--81. doi:10.1007/BF02385982. https://projecteuclid.org/euclid.afm/1485896544


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References

  • Adams, D. R., On the existence of capacitary strong type estimates in Rn, Ark. mat. 14 (1976), 125–140.
  • Adams, D. R., Meyers, N. G., Thinness and Wiener criteria for non-linear potentials, Indiana Univ. Math. J. 22 (1972), 169–197.
  • Adams, D. R., Meyers, N. G., Bessel potentials. Inclusion relations among classes of exceptional sets, Indiana Univ. Math. J. 22 (1973), 873–905.
  • Adams, D. R., Polking, J. C. The equivalence of two definitions of capacity, Proc. Amer. Math. Soc. 37 (1973), 529–534.
  • Aronszajn, N., Smith, K. T., Theory of Bessel potentials. Part I, Ann. Inst. Fourier 11 (1961), 385–475.
  • Bagby, T., Quasi topologies and rational approximation, J. Functional Analysis 10 (1972), 259–268.
  • Bagby, T., Ziemer, W. P., Pointwise differentiability and absolute continuity, Trans. Amer. Math. Soc. 191 (1974), 129–148.
  • Bers, L., An approximation theorem, J. Analyse Math. 14 (1965), 1–4.
  • Beurling, A., Deny, J., Dirichlet spaces, Proc. National Acad. Sci. 45 (1959), 208–215.
  • Burenkov, V. I., Approximation of functions in the space W ${}_{p}^{r}$ (Θ) by compactly supported functions for an arbitrary open set ω, Trudy Mat. Inst. im. V. A. Steklova AN SSSR, 131 (1974), 51–63.
  • Calderón, A. P., Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math. 4 (1961), 33–49.
  • Calderón, A. P., Zygmund, A., Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171–225.
  • Calderón, C. P., Fabes, E. B., Rivière, N. M., Maximal smoothing operators, Indiana Univ. Math. J. 23 (1974), 889–898.
  • Deny, J., Systèmes totaux de fonctions harmoniques, Ann. Inst. Fourier 1 (1965), 103–113.
  • Deny, J., Sur la convergence de certaines intégrales de la théorie du potentiel, Arch. der Math. 5 (1954), 367–370.
  • Deny, J. Méthodes hilbertiennes en théorie du potentiel, Potential Theory (C. I. M. E., I. Ciclo, Stresa 1969), 121–201, Ed. Cremonese, Rome 1970.
  • Fernström, C., Polking, J. C., Bounded point evaluations and approximation in Lp by solutions of elliptic partial differential equations, J. Functional Analysis, to appear.
  • Fuglede, B., Applications du théorème minimax à l'étude de diverses capacités, C. R. Acad. Sci. Paris. Sér. A 266 (1968), 921–923.
  • Havin, V. P., Approximation in the mean by analytic functions, Dokl. Akad. Nauk SSSR 178 (1968), 1025–1028.
  • Hedberg, L. I., Approximation in the mean by analytic functions, Trans. Amer. Math. Soc. 163 (1972), 157–171).
  • Hedberg, L. I., Non-linear potentials and approximation in the mean by analytic functions, Math. Z. 129 (1972), 299–319.
  • Hedberg, L. I., On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505–510.
  • Hedberg, L. I., Approximation in the mean by solutions of elliptic equations, Duke Math. J. 40 (1973), 9–16.
  • Lions, J. L., Magenes, E., Problèmes aux limites non homogènes IV. Ann. Scuola Norm. Sup. Pisa (3)15 (1961), 311–326.
  • Lions, J. L., Magenes, E., Problemi ai limiti non omogenei V. Ann. Scuola Norm. Sup. Pisa (3)16 (1962), 1–44.
  • Lions, J. L., Magenes, E., Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris 1968.
  • Littman, W., A connection between α-capacity and m-p polarity, Bull. Amer. Math. Soc. 73 (1967), 862–866.
  • Maz'ja, V. G., The Dirichlet problem for elliptic equations of arbitrary order in unbounded regions. Dokl. Akad. Nauk SSSR 150 (1963), 1221–1224.
  • Maz'ja, V. G., On (p, l)-capacity, imbedding theorems, and the spectrum of a selfadjoint elliptic operator, Izv. Akad. Nauk SSSR ser. mat. 37 (1973), 356–385.
  • Maz'ja, V. G., On the connection between two kinds of capacity, Vestnik Leningrad. Univ. 1974, No. 7, 33–40.
  • Maz'ja, V. G., Havin, V. P., Non-linear potential theory, Uspehi Mat. Nauk 27: 6 (1972) 67–138.
  • Maz'ja, V. G., Havin, V. P., Application of (p, l)-capacity to some problems in the theory of exceptional sets, Mat. Sb. 90 (132) (1973), 558–591.
  • Mel'nikov, M. S., Sinanjan, S. O., Problems in the theory of approximation of functions of one complex variable, Sovremennye problemy matematiki (ed. Gamkrelidze, R. V.), t. 4, 143–250 (Itogi nauki i tehniki), VINITI, Moscow 1975. (English translation: J. Soviet Math. 5 (1976), 688–752.)
  • Meyers, N. G., A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand. 26 (1970), 255–292.
  • Meyers, N. G., Taylor expansion of Bessel potentials. Indiana Univ. Math. J. 23 (1974), 1043–1049.
  • Meyers, N. G., Continuity properties of potentials, Duke Math. J. 42 (1975), 157–166.
  • Polking, J. C., Approximation in Lp by solutions of elliptic partial differential equations, Amer. Math. J. 94 (1972), 1231–1244.
  • Sinanjan, S. O., Approximation by analytic functions and polynomials in the areal mean, Mat. Sb. 69 (111), 546–578. (Amer. Math. Soc. Translations) (2)74 (1968), 91–124.
  • Sjödin, T., Bessel potentials and extension of continous functions on compact sets, Ark. Mat. 13 (1975), 263–271.
  • Stein, E. M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, N. J., 1970.
  • Triebel, H., Boundary values for Sobolev-spaces with weights. Density of D(ω) etc., Ann. Scuola Norm. Sup. Pisa (3)27 (1973), 73–96.
  • Wallin, H., Continuous functions and potential theory, Ark. mat. 5 (1963), 55–84.
  • Babuška, I., Stability of the domain with respect to the fundamental problems in the theory of partial differential equations, mainly in connection with the theory of elasticity I, II (Russian). Czechoslovak Math. J. 11 (86) (1961), 76–105, and 165–203.
  • Schulze, B.-W., Wildenhain, G., Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebiger Ordnung. Akademie-Verlag, Berlin, 1977.
  • Saak, È. M., A capacity condition for a domain with a stable Dirichlet problem for higher order elliptic equations, Mat. Sb. 100 (142) (1976), 201–209.