Interpolation of Operators: A Multiplier Theorem
In this chapter, we shall first study two basic results in interpolation of operators in L p spaces, the Riesz–Thorin theorem and the Marcinkiewicz interpolation theorem (diagonal case). As a consequence of the former we shall prove the Hardy-Littlewood-Sobolev theorem for Riesz potentials. In this regard, we need to introduce one of the fundamental tools in harmonic analysis, the Hardy–Littlewood maximal function. In Section 2.4 we shall prove the Mihlin multiplier theorem.