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Fractional integro-differentiation in harmonic mixed norm spaces on a half-space

Karen L. Avetisyan (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces h ( p , q , α ) 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 , α ) for the range 0 < p , 0 < q . As an application of the above, we give a characterization of h ( p , q , α ) by means of an integral representation with the use of Besov spaces.

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