References
P. R. Beesack, Hardy's inequality and its extensions, Pacific J. Math., 11 (1961), 39–61.
P. R. Beesack, Integral inequalities involving a function and its derivatives, Amer. Math. Monthly, 78 (1971), 705–741.
D. C. Benson, Inequality involving integrals of functions and their derivatives, J. Math. Anal. Appl., 17 (1967), 293–308.
J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull., 21 (1978), 405–408.
S. G. Kreîn, Ju. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Transl. Math. Monographs, A.M.S. 51 (1982).
R. T. Lewis, Singular elliptic operator of second order with purely discrete spectra, Trans. Amer. Math. Soc., 271 (1982), 653–666.
R. T. Lewis, A Friedrichs inequality and an application, Proc. Roy. Soc. Edinburgh. Sec. A, 97 (1984), 185–191.
V. G. Maz'ja, Sobolev Spaces, Springer-Verlag (Berlin, 1985).
B. Muckenhoupt, Hardy's inequality with weights, Studia Math., 44 (1972), 31–38.
B. Opic and A. Kufner, Hardy-type Inequalities, Longman Scientific and Technical, John Wiley & Sons, Inc. (New York 1990).
G. J. Sinnamon, A weighted gradient inequality, Proc. Roy. Soc. Edinburgh, 111A (1989), 329–335.
D. T. Shum, On a class of new inequalities, Trans. Amer. Math. Soc., 204 (1975), 299–341.
E. M. Stein and G. Weiss, Fourier Analysis on Euclidean Spaces, Princeton University Press (Princeton, N. J., 1971).
Author information
Authors and Affiliations
Additional information
Research supported in part by The American Univeraity in Cairo.
Rights and permissions
About this article
Cite this article
Emara, S.A.A. Weighted estimates involving a function and its derivatives. Acta Math Hung 72, 197–208 (1996). https://doi.org/10.1007/BF00050681
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00050681