Weighted Norm Inequalities and Homogeneous Spaces

Abstract

<p>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.</p> <p>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.</p> <p>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.</p> <p>The space of functions of bounded mean oscillation (BMO) is defined on a homogenous space. Under certain conditions BMO and BMOʳ (0</p>