Triebel H. Tempered Homogeneous Function Spaces

London, UK, European Mathematical Society, 2015. — 145 p. — (EMS Series of Lectures in Mathematics 21). — ISBN: 978-3-03719-155-2.This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of type Bsp,qBp,qs and Fsp,qFp,qs.Motivation and preliminaries
Motivation: Navier–Stokes equations
Heat kernels
Types of norms, homogeneity
Spaces on Sÿ0(Rn)
Basic definitions
The spaces Sÿ(Rn) and Sÿ0(Rn)
Definitions
Descriptions in terms of heat kernels
Further equivalent norms
Further tempered homogeneous spaces
New approach
Spaces with negative smoothness
Further properties
Spaces with positive smoothness
Duality
Interpolation
Lorentz spaces
Spaces with positive smoothness, revisited
Spaces with general smoothness
Haar bases
Pointwise multipliers
Truncations
Harmonic norms
Norms based on differences and derivatives
Lifts and further domestic norms
Lizorkin representations
Traces
Spaces on domains
Diversity
Beyond the distinguished strip, I
Beyond the distinguished strip, II
Local homogeneity for inhomogeneous spaces
On the q-dependence of some properties of Fs p;q-spaces