| The theory of interpolation of operators derives from the classical interpolation theorems of Marcel Riesz, G. Olof Thorin and Jozef Marcinkiewicz. Much of this theory can be described in terms of the families of Lebesgue spaces Lp and Lorentz spaces Lp,q. This theory is surveyed in Chapter 1 of the thesis.;More recent methods admit significant generalizations of the classical theory. In the second chapter we discuss the Hardy-spaces H p and BMO, the space of functions of bounded mean oscillation. In the final chapter, we describe the interpolation spaces for the pairs ( H1,Linfinity), (L 1,BMO) and (H1, BMO), following the treatments given by Nestor M. Riviere, Yoram Sagher; Colin Bennett, Robert Sharpley; and Ronald DeVore, respectively. |
