Introduction to besov and bessel potential spaces

The purpose of this thesis is to give a brief introduction to the modern theory of fuction spaces. More precisely, we study the scales of Besov and Bessel potential spaces, which generalize both the classical Hölder spaces and the Sobolev spaces. For this purpose a suitable Fourier analytic characterization using a dyadic partition unity in Fourier space is used. We study the relations between Besov and Bessel potential spaces and their relation to sobolev and Hölder spaces. Finally, boundedness of pseudodifferential operators on these spaces is shown.