JournalszaaVol. 26, No. 4pp. 473–480

On Ren-Kähler's Paper &#34;Hardy-Littlewood Inequalities and <em>Q<sub>p</sub></em>-Spaces&#34;, <em>Z. Anal. Anwendungen</em> 24 (2005), 375 – 388

  • Stevo Stevic

    Serbian Academy of Science, Beograd, Serbia
On Ren-Kähler's Paper &#34;Hardy-Littlewood Inequalities and <em>Q<sub>p</sub></em>-Spaces&#34;, <em>Z. Anal. Anwendungen</em> 24 (2005), 375 – 388 cover
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Abstract

In this note we prove that a harmonic function uu on the unit ball B\RRnB\subset\RR^n belongs to the harmonic mixed norm space Asp,q(B),{\cal A}^{p,q}_s(B), when p,q(0,]p,q\in (0,\infty] and s>0s>0, if and only if all weighted tangential derivatives of order kk (with positive orders of derivatives) belong to the related weighted Lebesgue mixed norm space Lsp,q(B).{\cal L}^{p,q}_s(B). Our proof of the result for the case q(0,1)q\in (0,1) and kk is odd, corrects the corresponding one in the paper: G.~Ren and U.~K\"ahler, Hardy-Littlewood inequalities and QpQ_p-spaces, {\it Z. Anal. Anwendungen} {24} (2005), 375 -- 388.

Cite this article

Stevo Stevic, On Ren-Kähler's Paper &#34;Hardy-Littlewood Inequalities and <em>Q<sub>p</sub></em>-Spaces&#34;, <em>Z. Anal. Anwendungen</em> 24 (2005), 375 – 388. Z. Anal. Anwend. 26 (2007), no. 4, pp. 473–480

DOI 10.4171/ZAA/1337