Weighted norm inequalities for integral transforms

Abstract

Weighted (L p , L q ) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón-type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the conditions on weights is discussed. © Indiana University Mathematics Journal.