Date of Award
9-1986
Degree Type
Thesis
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Supervisor
Professor H.P. Heinig
Abstract
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.
Recommended Citation
Emara, Salah Abbas Ahmed, "Mixed Weighted Inequalities For Classes of Operators" (1986). Open Access Dissertations and Theses. Paper 2220.
http://digitalcommons.mcmaster.ca/opendissertations/2220