Interpolation of Operators. A Multiplier Theorem
In this chapter we shall first study two basic results in interpolation of operators in Lp 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.
KeywordsSimple Function Weak Type Interpolation Theorem Riesz Potential Multiplier Theorem
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