Abstract
For a class of integral transforms T φ over ℝ n , a sufficient condition is given which ensures that T φ is bounded between weighted Lebesgue spaces. We also obtain a necessary and sufficient condition when the Hardy integral transform H of one of the weights is doubling. In such a case, the boundedness of T φ and the boundedness of H are equivalent. The class of transforms considered here includes the Stieltjes transform, the Laplace transform, and the Lambert transform over ℝ n .
2000 Mathematics Subject classification :
Acknowledgements
This research is supported in part by I-Shou University, Kaohsiung, ROC, under Grant ISU98-02-15.