Gentle Invitation to the Fractional World

The book focuses on the basic theory of nonlocal and fractional operators and it is divided into two main parts covering respectively the basic theory of the "singular-integral" fractional Laplacian operator, which also includes a number of explicit examples of its evaluations, and the regularity theory in L^p spaces, by going through Bessel and Besov spaces. A number of appendices then go over additional material in order to make the exposition as self-contained as possible.The book is suitable for a PhD course but can be also read by advanced undergraduates. It contains didactic elements, but it is also useful for researchers, since it collects essential material in a concise and self-constrained way.