| This thesis contains results in three directions in the study of harmonic analysis on weighted spaces. The first result shows that studying the Ap,q condition for a matrix-valued weight cannot generally be reduced to studying a collection of related scalar weights. This result makes some use of space filling curves, and the way in which the curves are used may be interesting in its own right. The second result provides bounds on a maximal function for weights on functions taking values in a Banach space, assuming the weights satisfy a reverse Holder condition. The third result is a variant of the Calderon-Zygmund decomposition for weights satisfying the reverse Holder condition that allows us to extend some known results when p = 2 to other exponents. |
