# Tempered Homogeneous Function Spaces

### Hans Triebel

University of Jena, Germany

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If one tries to transfer assertions for the inhomogeneous spaces $A_{p,q}(R_{n})$, $A∈{B,F}$, appropriately to their homogeneous counterparts $A∗_{p,q}(R_{n})$ within the framework of the dual pairing $(S(R_{n}),S_{′}(R_{n}))$ then it is hard to make a mistake as long as the parameters $p,q,s$ are restricted by $0<p,q≤∞$ and, in particular, $n(p1 –1)<s<pn $. It is the main aim of these notes to say what this means.

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 $B_{p,q}$ and $F_{p,q}$.