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Keywords:
embedding theorems; integral representations; conjugation; projections
embedding theorems; integral representations; conjugation; projections
Summary:
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\leq \infty $, $0<q\leq \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.
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