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Interpolation of Operators: A Multiplier Theorem

  • Felipe LinaresEmail author
  • Gustavo Ponce
Chapter
Part of the Universitext book series (UTX)

Abstract

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.

Keywords

Weak Type Interpolation Theorem Riesz Potential Multiplier Theorem Sublinear Operator 
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Copyright information

© Springer-Verlag New York 2015

Authors and Affiliations

  1. 1.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil
  2. 2.Dept. MathematicsUniversity of California, Santa Barbara College of Letters & ScienceSanta BarbaraUSA

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