Harmonic Analysis, Sobolev space and some of it's Characterization

Two of the most useful tools for studying PDE are Sobolev space and Harmonic analysis. In this talk we will go over some elementary facts about Sobolev space and Harmonic analysis. Our main goal will be to look at Sobolev space using tools from Harmonic analysis. In particular, we will build up the Littlewood-Paley theorem and see how they help us to characterize Inhomogeneous Sobolev spaces.