This is a preview of subscription content, log in via an institution to check access.
Literature cited
M. Riesz, “Sur les fonctions conjuguées,” Math. Z.,27, 218–244 (1927).
G. H. Hardy and J. E. Littlewood, “Some properties of conjugate functions,” J. Reine Angew. Math.,167, 405–432 (1932).
E. Stein and G. Weiss, “On the theory of harmonic functions of several variables,” Acta Math.,103, Nos. 1–2, 25–62 (1960).
C. Fefferman and E. Stein, “HP spaces of several variables,” Acta Math.,129, Nos. 3–4, 137–193 (1972).
T. M. Fleet, “Inequalities for the p-th mean values of harmonic and subharmonic functions withp⩽1, “ Proc. London Math. Soc., Ser. 3,20, 249–275 (1970).
A. P. Calderon and A. Zygmund, “On higher gradients of harmonic functions,” Stud. Math.,24, No. 2, 211–226 (1964).
U. Kuran, “Classes of subharmonic functions inR n × (0, ∞), ” Proc. London Math. Soc., Ser. 3,16, 473–492 (1966).
A. A. Bonami, “Integral inequalities for conjugate harmonic functions of several variables,” Mat. Sb.,87, No. 2, 188–203 (1972).
J. Horvath, “Sub les fonctions conjuguées á plusieurs variables,” Proc. Koince Nederl. Acad. Wetensch., Ser. A,56, No. 1, 17–29 (1953).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 31, No. 1, pp. 25–32, January, 1982.
Rights and permissions
About this article
Cite this article
Ryabogin, A.K. Integral inequalities for conjugate harmonic functions. Mathematical Notes of the Academy of Sciences of the USSR 31, 14–18 (1982). https://doi.org/10.1007/BF01146261
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01146261