Hölder Integral Inequality
If
with
, 
, then
with equality when
If
, this inequality becomes Schwarz's Inequality.
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 11, 1972. Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1099, 1993. Hölder, O. ``Über einen Mittelwertsatz.'' Göttingen Nachr., 44, 1889. Riesz, F. ``Untersuchungen über Systeme integrierbarer Funktionen.'' Math. Ann. 69, 456, 1910. Riesz, F. ``Su alcune disuguaglianze.'' Boll. Un. Mat. It. 7, 77-79, 1928. Sansone, G. Orthogonal Functions, rev. English ed. New York: Dover, pp. 32-33, 1991.
- CLEAN Map
- Clebsch-Aronhold Notation
- Clebsch Diagonal Cubic
- Clebsch-Gordan Coefficient
- Clement Matrix
- Clenshaw Recurrence Formula
- Clifford Algebra
- Clifford's Circle Theorem
- Clifford's Curve Theorem
- Cliff Random Number Generator
- Clique
- Clique Number
- Clock Solitaire
- Closed Curve
- Closed Curve Problem
- Closed Disk
- Closed Form
- Closed Graph Theorem
- Closed Interval
- Closed Set
- Close Packing
- Closure
- Clothoid
- Clove Hitch
- Clump