Weighted norm inequalities for fractional integrals

The principal problem considered is the determination of all nonnegative functions, V ( x ) V(x) , such that ‖ T γ f ( x ) V ( x ) ‖ q ≤ C ‖ f ( x ) V ( x ) ‖ p \|{T_γ }f(x)V(x) \|_q ≤ C \|f(x)V(x) \|_p where the functions are defined on R n , 0 > γ > n , 1 > p > n / γ , 1 / q = 1 / p − γ / n {R^n},0 > γ > n,1 > p > n/γ ,1/q = 1/p - γ /n , C is a constant independent of f and T γ f ( x ) = ∫ f ( x − y ) | y | γ − n