(Hölder's Inequality

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 71E
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Theorem 8.6. (Hölder's Inequality for 0 <p< 1). Let 0 <p<|
and q be the index conjugate to p. If fe L' and ge L' then
1/p
JI f(x) g(x) I dx 2JI f(x) d x
E
I g(x) 1ª dx
E
E
abl
JIg(x) I' dx # 0.
E
provided
Transcribed Image Text:Theorem 8.6. (Hölder's Inequality for 0 <p< 1). Let 0 <p<| and q be the index conjugate to p. If fe L' and ge L' then 1/p JI f(x) g(x) I dx 2JI f(x) d x E I g(x) 1ª dx E E abl JIg(x) I' dx # 0. E provided
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