5: any help in any question, will be much appreciated.
Last edited by mr fantastic; Oct 3rd 2009 at 10:30 PM. Reason: Moved from another thread
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By choosing $\displaystyle f\in L^p(X,\mu)$ with $\displaystyle ||f||_{L^p(X,\mu)}=1$, a simple application of the Holder inequality will give you $\displaystyle ||Af||_{L^p(X,\mu)}\leq ||K||_{L^p(X\times Y,\mu\times \nu)}$.
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