# Thread: Proving a bounded operator

1. ## Proving a bounded operator

5:

any help in any question, will be much appreciated.

2. By choosing $f\in L^p(X,\mu)$ with $||f||_{L^p(X,\mu)}=1$, a simple application of the Holder inequality will give you
$||Af||_{L^p(X,\mu)}\leq ||K||_{L^p(X\times Y,\mu\times \nu)}$.