I have already read the standard part in Evan's PDE text book. However, in his book, the theorems like Sobolev embeddings only involve bounded domain, and it talks just a little about fractional Sobolev spaces. I want to look at a book that is deeper than this. I know the book written by Adams is a standard book, but this book is much more than what I need right now. Can someone recommend me a book for Sobolev space that is readable? Thanks in advance.
2026-04-08 09:27:14.1775640434
Book recommendation: Sobolev spaces.
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G. Folland's TATA lectures on PDE give a terrific quick-intro to Sobolev spaces on $\mathbb R^n$, via Fourier transforms. That was what finally convinced me that the idea was useful. :) The possibility of using Fourier transforms "globally" is a great simplifier.
It is also possible to do "global" Sobolev theory on (products of) circles, via Fourier series. Obviously, this will be even simpler than the Fourier transform scenario.