Sobolev Spaces and Pseudo-Differential Operators
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.
KeywordsSobolev Space Pseudodifferential Operator Principal Symbol Distribution Sense Leibniz Rule
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