Weighted norm inequalities for singular and fractional integrals

Abstract:

Inequalities of the form ${\left \| {{{\left | x \right |}^\alpha }Tf} \right \|_q} \leqq C{\left \| {{{\left | x \right |}^\alpha }f} \right \|_p}$ are proved for certain well-known integral transforms, T, in ${E^n}$. The transforms considered include Calderón-Zygmund singular integrals, singular integrals with variable kernel, fractional integrals and fractional integrals with variable kernel.