Sobolev Spaces and Pseudo-Differential Operators

Part of the Universitext book series (UTX)

In this chapter we will give a brief introduction to the classical Sobolev spaces Hs(Rn). Sobolev spaces measure the differentiability of functions in L2(Rn) and they are a fundamental tool in the study of partial differential equations.We also will list some basic facts of the theory of pseudo-differential operators without proof. This will be useful to study smoothness properties of solutions of dispersive equations.


Sobolev Space Pseudodifferential Operator Principal Symbol Distribution Sense Leibniz Rule 


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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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