Electron. J. Diff. Equ., Vol. 2011 (2011), No. 74, pp. 1-10.

Young's integral inequality with upper and lower bounds

Douglas R. Anderson, Steven Noren, Brent Perreault

Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding results for difference equations are given, and several examples are included. We extend these results to piecewise-monotone functions as well.

Submitted February 14, 2011. Published June 15, 2011.
Math Subject Classifications: 26D15, 39A12, 34N05.
Key Words: Young's inequality; monotone functions; Pochhammer lower factorial; difference equations; time scales.

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Douglas R. Anderson
Concordia College, Department of Mathematics and Computer Science
Moorhead, MN 56562, USA
email: andersod@cord.edu   http://www.cord.edu/faculty/andersod/
Steven Noren
Concordia College
Moorhead, MN 56562, USA
email: srnoren@cord.edu
Brent Perreault
Concordia College
Moorhead, MN 56562, USA
email: bmperrea@cord.edu

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