By Robert A. Adams and John J. F. Fournier
Includes reviews of real analysis and an extensive treatment of Lebesgue spaces.
Develops at length the intrinsic definition and properties of Sobolev spaces, in particular their imbedding, compact imbedding, interpolation and extension properties.
Provides a thorough treatment of the real interpolation method and its application to Lorentz and Besov spaces.
Includes surveys of other fractional-order spaces (Bessel potentials, Triebel-Lizorkin).
Develops the theory of Orlicz and Orlicz-Sobolev spaces and their imbeddings.
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.
This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.