Weighted norm inequalities for integral transforms with splitting kernels

We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted Lᵖ-Lq spaces, with 1 p q. The kernels K (x, y) of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable. The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the H_ (or Struve) transform in the case >12, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases p=1 or q=.