K.L. Avetisyan
Fractional integro-differentiation in harmonic mixed norm spaces on a half-space

Comment.Math.Univ.Carolinae 42,4 (2001) 691-709.

Abstract: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.

Keywords: embedding theorems, integral representations, conjugation, projections
AMS Subject Classification: Primary 31B05; Secondary 31B10, 26A33