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On some reverse integral inequalities

Part of: Inequalities

Published online by Cambridge University Press:  09 April 2009

Luciana Nania
Luciana Nania
Affiliation:
Dipartimento di Matematica e Applicazioni“R. Caccioppoli” Via Mezzocannone 8, 80134 Napoli, Italy
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Abstract

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We prove the higher integrability of nonnegative decreasing functions, verifying a reverse inequality, and we calculate the optimal integrability exponent for these functions.

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 319 - 326
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bojarski, B. and Iwaniec, T., ‘Analytical foundations of the theory of quasi conformal mapping in Rn’ Ann. Acad. Sci. Fenn. Ser. AI Math. 8 (1983), 257–324.Google Scholar
[2]Gehring, F. W., ‘The Lρ integrability of the partial derivatives of a quasi conformal mapping’, Ada Math. 130 (1973), 265–277.Google Scholar
[3]Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, (Cambridge Univ. Press, 1964).Google Scholar
[4]Muckenhoupt, B., ‘Weighted norm inequalities for the Hardy maximal function’, Trans. Amer. Math. Soc. 165 (1972), 207–226.CrossRefGoogle Scholar
[5]Sbordone, C., ‘Higher integrability from reverse integral inequalities’, Proc. Internal. Meeting—Methods of Functional Analysis and Theory of Elliptic Equations, (Napoli, Liguori, 1983).Google Scholar
[6]Sbordone, C., ‘Rearrangement of functions and reverse Hölder inequalities’, Ennio de Giorgi Colloqium, pp. 134–146, Paris, 1983 (Pitman Res. Notes in Math. 125, 1985).Google Scholar