Literature Cited
G. C. Evans, “Potentials and positively infinite singularities of harmonic functions,” Monatsh. Math.,43, 419–424 (1936).
J. Deny, “Sur les infinis d'un potentiel,” Compt. Rend. Acad. Sci.,224, 524–525 (1947).
J. Du Plessis, “A theorem about fractional integrals,” Proc. Amer. Math. Soc.,3, No. 6, 892–898 (1952).
J. Deny, “Sur la convergence de certaines intégrales de la théorie du potentiel,” Arch. Math.,5, Nos. 4–6, 367–370 (1954).
N. Du Plessis, “Some theorems about the Reisz fractional integral,” Trans. Amer. Math. Soc.,80, No. 1, 124–134 (1955).
G. Choquet, “Sur les Gδ de capacité nulle,” Ann. Inst. Fourier,9, 103–110 (1959).
B. Fuglede, “On generalized potentials of functions in the Lebesgue class,” Math. Scand.,8, 287–304 (1960).
N. S. Landkof, Fundamentals of Potential Theory [in Russian], Nauka, Moscow (1966).
Yu. G. Reshetnyak, “On the notion of capacity in the theory of functions with generalized derivatives,” Sib. Matem. Zb.,10, No. 5, 1109–1138 (1969).
N. Meyers, “A theory of capacities for potentials of functions in Lebesgue classes,” Math. Scand.,26, No. 2, 255–292 (1970).
B. W. Martin, “On α-potentials of functions in Lp classes,” J. London Math. Soc.,2, 699–708 (1970).
S. P. Preobrazhenskii, “On divergence sets of integrals of potential type with densities from Lp,” Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Akad. Nauk SSSR,22, 196–198 (1971).
H. Wallin, “Riesz potentials, k,p-capacity, and p-modules,” Michigan Math. J.,18, No. 2, 257–263 (1971).
J. Deny, “Les potentiels d'énergie finie,” Acta Math.,82, 107–183 (1950).
V. G. Maz'ya and V. P. Khavin, “A nonlinear analog of the Newton potential and metric properties of (p,l)-capacity,” Dokl. Akad. Nauk SSSR,194, No. 4, 770–773 (1970).
V. G. Maz'ya and V. P. Khavin, “Nonlinear potential theory,” Usp. Matem. Nauk,27, No. 6, 67–138 (1972).
D. R. Adams and N. G. Meyers, “Thinness and Wiener criteria for nonlinear potentials,” Indiana Univ. Math. J.,22, No. 2, 139–158 (1972).
D. Adams and N. Meyers, “Bessel potentials. Inclusion relations among classes of exceptional sets,” Indiana Univ. Math. J.,22, No. 9, 873–905 (1973).
G. G. Hardy, D. E. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 2, pp. 347–354, March–April, 1975.
Rights and permissions
About this article
Cite this article
Preobrazhenskii, S.P. Divergence sets of integrals of potential type with densities from Lp . Sib Math J 16, 268–274 (1975). https://doi.org/10.1007/BF00967511
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967511