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

Karen L. Avetisyan

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 691-709
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Avetisyan, Karen L.. "Fractional integro-differentiation in harmonic mixed norm spaces on a half-space." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 691-709. <http://eudml.org/doc/248800>.

@article{Avetisyan2001,
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\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.},
author = {Avetisyan, Karen L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {embedding theorems; integral representations; conjugation; projections; mixed norm spaces; harmonic functions; fractional derivative; fractional integration},
language = {eng},
number = {4},
pages = {691-709},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fractional integro-differentiation in harmonic mixed norm spaces on a half-space},
url = {http://eudml.org/doc/248800},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Avetisyan, Karen L.
TI - Fractional integro-differentiation in harmonic mixed norm spaces on a half-space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 691
EP - 709
AB - 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.
LA - eng
KW - embedding theorems; integral representations; conjugation; projections; mixed norm spaces; harmonic functions; fractional derivative; fractional integration
UR - http://eudml.org/doc/248800
ER -

References

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  25. Avetisyan K.L., Fractional integration and integral representations in weighted classes of harmonic functions, Analysis Math. 26 (2000), 161-174. (2000) Zbl0997.30030MR1792883

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