Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Reduction of Opial-type inequalities to norm inequalities

Author: Gord Sinnamon
Journal: Proc. Amer. Math. Soc. 132 (2004), 375-379
MSC (2000): Primary 26D15
Published electronically: September 5, 2003
MathSciNet review: 2022358
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Weighted Opial-type inequalities are shown to be equivalent to weighted norm inequalities for sublinear operators and for nearly positive operators. Examples involving the Hardy-Littlewood maximal function and the nonincreasing rearrangement are presented.

References [Enhancements On Off] (What's this?)

  • 1. C. Bennett and R. Sharpley, Interpolation of Operators, Pure and Applied Mathematics, Vol. 129, Academic Press, Boston, MA, 1988. MR 89e:46001
  • 2. S. Bloom, First and second order Opial inequalities, Studia Math. 126 (1997), 27-50. MR 98g:26016
  • 3. R. C. Brown, A. M. Fink, and D. B. Hinton, Some Opial, Lyapunov, and De la Valée Poussin inequalities with nonhomogeneous boundary conditions, J. Inequal. Appl. 5 (2000), 11-37. MR 2000m:34073
  • 4. G. Sinnamon, Weighted Hardy and Opial-type inequalities, J. Math. Anal. Appl. 160 (1991), 434-445. MR 92f:26037
  • 5. V. D. Stepanov, The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc., 338 (1993), 173-186. MR 93j:26012
  • 6. A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando, FL, 1986. MR 91m:42001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26D15

Retrieve articles in all journals with MSC (2000): 26D15

Additional Information

Gord Sinnamon
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

Keywords: Opial inequality, Opial-type inequality, weight
Received by editor(s): July 19, 2002
Published electronically: September 5, 2003
Additional Notes: Supported by the Natural Sciences and Engineering Research Council of Canada
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society