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a)<math>|h(x)| \leq (\int |f|^p)^(1/p)(\int |g|^q)^(1/q)</math>
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a)<math>|h(x)| \leq (\int |f(x-y)|^p dy)^(1/p)(\int |g(y)|^q dy)^(1/q) = (\int |f(z)|^p dz)^(1/p)(\int |g(y)|^q dy)^(1/q) \leq ||f||_{p}||g||_{q}</math>

Revision as of 14:13, 22 July 2008

a)$ |h(x)| \leq (\int |f(x-y)|^p dy)^(1/p)(\int |g(y)|^q dy)^(1/q) = (\int |f(z)|^p dz)^(1/p)(\int |g(y)|^q dy)^(1/q) \leq ||f||_{p}||g||_{q} $

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal