Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls
HTML articles powered by AMS MathViewer
- by Aleksandra Čižmešija, Josip Pečarić and Ivan Perić PDF
- Proc. Amer. Math. Soc. 128 (2000), 2543-2552 Request permission
Abstract:
Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in $\mathbf { R}^n$ centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin–Cochran–Lee inequalities and their companion results for $n$-dimensional balls. Finally, the best possible constants for these inequalities are obtained.References
- Michael Christ and Loukas Grafakos, Best constants for two nonconvolution inequalities, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1687–1693. MR 1239796, DOI 10.1090/S0002-9939-1995-1239796-6
- James A. Cochran and Cheng Shyong Lee, Inequalities related to Hardy’s and Heinig’s, Math. Proc. Cambridge Philos. Soc. 96 (1984), no. 1, 1–7. MR 743695, DOI 10.1017/S0305004100061879
- A. Čižmešija and J. Pečarić, Mixed means and Hardy’s inequality, Math. Inequal. Appl. 1, No. 4 (1998), 497–506.
- Pavel Drábek, Hans P. Heinig, and Alois Kufner, Higher-dimensional Hardy inequality, General inequalities, 7 (Oberwolfach, 1995) Internat. Ser. Numer. Math., vol. 123, Birkhäuser, Basel, 1997, pp. 3–16. MR 1457264
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- V. Levin, O neravenstvah III: Neravenstva, vypolnjaemie geometričeskim srednim neotricatel’noi funkcii, Math. Sbornik 4 ( 46) (1938), 325–331.
- E. R. Love, Inequalities related to those of Hardy and of Cochran and Lee, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 3, 395–408. MR 830353, DOI 10.1017/S0305004100064343
- D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Mathematics and its Applications (East European Series), vol. 53, Kluwer Academic Publishers Group, Dordrecht, 1991. MR 1190927, DOI 10.1007/978-94-011-3562-7
- Gou Sheng Yang and Yü Jên Lin, On companion inequalities related to Heinig’s, Tamkang J. Math. 22 (1991), no. 4, 313–322. MR 1143519
Additional Information
- Aleksandra Čižmešija
- Affiliation: Department of Mathematics, University of Zagreb, Bijeničkacesta 30, 10000 Zagreb, Croatia
- Email: cizmesij@math.hr
- Josip Pečarić
- Affiliation: Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
- Email: pecaric@mahazu.hazu.hr
- Ivan Perić
- Affiliation: Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
- Received by editor(s): September 28, 1998
- Published electronically: December 7, 1999
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2543-2552
- MSC (2000): Primary 26D10, 26D15
- DOI: https://doi.org/10.1090/S0002-9939-99-05408-8
- MathSciNet review: 1676291