Geodesic
Fractional integro-differentiation in harmonic mixed norm spaces on a half-space
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 691-709.

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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 $0$, $0$. 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.
Classification : 26A33, 31B05, 31B10, 31C05
Keywords: embedding theorems; integral representations; conjugation; projections 
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     title = {Fractional integro-differentiation in harmonic mixed norm spaces on a half-space},
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Avetisyan, K. L. Fractional integro-differentiation in harmonic mixed norm spaces on a half-space. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 691-709. http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a9/