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_ 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 Rⁿ, 0 > > n, 1 > p > n/, 1/q = 1/p - /n, C is a constant independent of f and T γ f (x) = ∫ f (x − y) | y | γ − n