Date of Award
Doctor of Philosophy (PhD)
Doctor H.P. Heinig
This thesis considers weighted norm inequalities. We characterize those pairs of weight functions for which a mixed norm version of the Hardy inequalities hold and apply these results to certain well known operators.
The two weight problem for weak boundedness of certain fractional maximal functions is solved and we give a new necessary condition for strong type boundedness of the fractional maximal and fractional integral operators. Under an additional assumption our condition is shown to be sufficient.
Many of these results are true in the setting of the homogeneous spaces of Calderon. Proofs of this together with some L log L type results are given.
The space of functions of bounded mean oscillation (BMO) is defined on a homogenous space. Under certain conditions BMO and BMOʳ (0
Bradley, John Scott, "Weighted Norm Inequalities and Homogeneous Spaces" (1979). Open Access Dissertations and Theses. Paper 668.