"A self-contained text providing all the basics of fractional Sobolev spaces. The book provides the background and relevant theory with explanations, alternatives and comparisons, and includes discussion of the Hardy and Rellich inequalities, first in classical format and then in fractional versions. Ideal for researchers and graduate students"--

D. E. Edmunds was Professor of Mathematics at Sussex University for twenty-six years; now Emeritus. He has co-authored nine books and written more than 230 papers. Honours include the LMS Pólya Prize, the Czech Academy of Sciences Bolzano Medal and the Medal for Mathematics of the Czech Mathematical Society.

1. Preliminaries; 2. Classical Sobolev spaces; 3. Fractional Sobolev spaces; 4. Eigenvalues of the fractional p-Laplacian; 5. Classical (local) Hardy inequalities; 6. Fractional analogues; 7. Classical and fractional inequalities of Rellich type; References; Symbol index; Author index; Index of terms.