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How can I give a bound on the $L^2$ norm of this function?
For $f\in L^p((1,\infty),m)$, $2 , Want to prove that there exists $C$ which only depends on $p$, such that $V(f,x)=\frac{1}{x}\int^{10x}_x\frac{f(t)}{t^{\frac{1}{4}}}dm(t)$ satisfies $||V(f,x)||_{L^2((1,\infty),m)}\le C||f||_{L^p((1,\infty),m)}$