Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.

This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate cours

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is es

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already

Focusing on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds, this