Lecture 14 H Olders Inequality Anthony Erb Lugo March 12 2011 I

Lecture Olders Inequality Anthony Erb Lugo March 2011 This Lecture Well Cover Several Applications Olders Inequality Before Begin Its Recommended

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Lecture 14 H Olders Inequality Anthony Erb Lugo March 12 2011 In This Lecture Well Cover Several Applications Of H Olders Inequality Before We Begin Its Recommended To The Reader To Be Familiar With The Following Inequalities Trivial Inequality Arithmetic Mean Geometric Mean And The Cauchy Schwarz Inequality If The Reader Is Not Familiar With These Inequalities It Is Then Advised To Read A Brief Introduction To Inequalites Lecture 7 In The OMC Archive 1 The Cauchy Schwarz Inequality Generalized Lets Recall The Cauchy Schwarz Inequality Theorem 1 1 The Cauchy Schwarz Inequality Leta 1 A 2 A N B 1 B 2 B N Be Real Numbers Then A 2 1 A 2 2 A 2 N B 2 1 B 2 2 B 2 N ≥ A 1 B 1 A 2 B 2 A N B N 2 With Equality If And Only If A 1 B 1 A 2 B 2 A N B N We Note That In The Cauchy Schwarz Inequality The Left Hand Side Has Two Products Where The Terms Inside Are Elevated To The Second Power

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