Advanced Search

In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces $h(p,q,\alpha )$ on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in $h(p,q,\alpha )$ for the range $0<p\le \infty$, $0<q\le \infty$. As an application of the above, we give a characterization of $h(p,q,\alpha )$ by means of an integral representation with the use of Besov spaces.