Mixed Weighted Inequalities For Classes of Operators

Abstract

<p>This thesis is concerned with the study of weighted inequalities for operators defined on certain function spaces. If T is a linear - or sublinear operator, weakly bounded on some endpoint spaces, then it is shown that T is also hounded on weighted intermediate spaces. Since the weights govern the indices of the spaces, our results yield weighted extensions of known interpolation spaces and consequently weighted norm inequalities for many classical operators over an extended range of indices. Specifically we obtain new weighted estimates for certain generalizations of the Fourier- and Laplace-transforms, namely the Hankel-, K- and ʯ-transforms in Lebesgue and Lorentz spaces.</p>