Tempered Homogeneous Function Spaces

  • Hans Triebel

    University of Jena, Germany
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If one tries to transfer assertions for the inhomogeneous spaces Ap,qs(Rn)A^s_{p,q} (\mathbb R^n), A{B,F}A \in \{B,F \}, appropriately to their homogeneous counterparts Ap,qs(Rn){\overset {\, \ast}{A}}{}^s_{p,q} (\mathbb R^n) within the framework of the dual pairing (S(Rn),S(Rn))\big( S(\mathbb R^n), S'(\mathbb R^n) \big) then it is hard to make a mistake as long as the parameters p,q,sp,q,s are restricted by 0<p,q0 < p,q \le \infty and, in particular, n(1p1)<s<npn(\frac {1}{p} – 1) < s < \frac {n}{p}. 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 Bp,qsB^s_{p,q} and Fp,qsF^s_{p,q}.