Clarkson's inequalities are a set of mathematical inequalities that relate to norms in functional spaces, particularly in the context of \( L^p \) spaces. They describe how the \( L^p \) norm of sums of functions behaves in relation to the norms of the individual functions.
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For , the Clarkson inequality isFor and , the other Clarkson inequality isTogether these inequalities prove uniform convexity of for .