Runst T. Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

De Gruyter, 2011. — 556 p.Introduction
Function spaces of Besov-Triebel-Lizorkin type
Definitions and fundamental properties
Embeddings
Some equivalent characterizations of Fsp,qand Bsp,q
Spaces on domains
Interpolation
Homogeneous spaces and a further supplement
Regular elliptic boundary value problems
Definitions and preliminaries
Estimates of integral operators
Estimates of the Poisson integral
A priori estimates
Regular elliptic boundary value problems
Pointwise multiplication
Introduction
The definition of the product
Necessary conditions for pointwise multiplication
Products of a function and a distribution
Products of functions and a distribution. The general case
The case of constant p
The extremal case p1 = p and p2 =.
Generalized Holder inequalities
The spaces Asp,q,unif and relations to M(Asp,q)
Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
Introduction
Nemytskij operators in Lebesgue and Sobolev spaces
The Composition operator corresponding to a C.-function G in and Bsp