WEIGHTED ESTIMATES FOR THE HANKEL TRANSFORM TRANSPLANTATION OPERATOR

抄録

The Hankel transform transplantation operator is investigated by means of a suitably established local version of the Calderón-Zygmund operator theory. This approach produces weighted norm inequalities with weights more general than previously considered power weights. Moreover, it also allows to obtain weighted weak type (1,1) inequalities, which seem to be new even in the unweighted setting. As a typical application of the transplantation, multiplier results in weighted $L^p$ spaces with general weights are obtained for the Hankel transform of any order greater than -1 by transplanting cosine transform multiplier results.