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Interpolation of Operators. A Multiplier Theorem

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

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.

Keywords

Simple Function Weak Type Interpolation Theorem Riesz Potential Multiplier Theorem 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Instituto Nacional deMatemática Pura e Aplicada (IMPA)Rio de Janeiro-RJBrazil
  2. 2.Department MathematicsUniversity of CaliforniaSanta BarbaraUSA

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