# Tempered Homogeneous Function Spaces

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*Hans Triebel*

A publication of the European Mathematical Society

This book deals with homogeneous function spaces of
Besov–Sobolev type within the framework of tempered
distributions in Euclidean \(n\)-space based on
Gauss–Weierstrass semi-groups. Related Fourier-analytical
descriptions and characterizations in terms of derivatives and
differences are incorporated after as so-called domestic norms.
This approach avoids the usual ambiguities modulo polynomials when
homogeneous function spaces are considered in the context of
homogeneous tempered distributions.

These notes are addressed to graduate students and mathematicians
having a working knowledge of basic elements of the theory of function
spaces, especially of Besov–Sobolev type. In particular, the
book might be of interest for researchers dealing with (nonlinear)
heat and Navier–Stokes equations in homogeneous function
spaces.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in tempered distributions and homogeneous function spaces.