## Harmonic Analysis

If $\displaystyle (I_{\alpha}f)(x) = \int_{\bold{R}^{n}} [V(x,y)]^{-1+ \alpha} f(y) \ d \mu(y)$ prove that $\displaystyle ||I_{\alpha} f||_{q} \leq A_{p,q} ||f||_{p}$ whenever $\displaystyle 1 < p < q < \infty$ and $\displaystyle q^{-1} = p^{-1} - \alpha$.