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5. Let (α1,α2,...,ân) and (b1,b2,...,bn) be two n-tuples 1 1 bers and let p, q be two positive real numbers such that + of indices is called a pair of conjugate indices.) Then the inequality p q 1/p P |Σα|= (Σ11)" (Σ11) j=1 j=1 j=1 19 1/9 " = 1. (

5. Let (α1,α2,...,ân) and (b1,b2,...,bn) be two n-tuples 1 1 bers and let p, q be two positive real numbers such that + of indices is called a pair of conjugate indices.) Then the inequality p q 1/p P |Σα|= (Σ11)" (Σ11) j=1 j=1 j=1 19 1/9 " = 1. (

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Let (a₁, a2,...‚an) and (b₁,b2,...,bn) be two n-tuples of real 1 1 numbers and let p, q be two positive real numbers such that + = 1. (Such a pair of indices is called a pair of conjugate indices.) Then the inequality P 9 n n 1/q n 1/p Σªb;|≤ ([«;l”)¹([Þ;")¹, j=1 j=1 j=1 holds. Moreover this is an equality if and only if |aj|P = X|bj|ª, 1 ≤ j ≤ n, for some real constant X.
Transcribed Image Text:5. Let (a₁, a2,...‚an) and (b₁,b2,...,bn) be two n-tuples of real 1 1 numbers and let p, q be two positive real numbers such that + = 1. (Such a pair of indices is called a pair of conjugate indices.) Then the inequality P 9 n n 1/q n 1/p Σªb;|≤ ([«;l”)¹([Þ;")¹, j=1 j=1 j=1 holds. Moreover this is an equality if and only if |aj|P = X|bj|ª, 1 ≤ j ≤ n, for some real constant X.
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