On Ren-Kähler's paper "Hardy-Littlewood inequalities and Q p-spaces" (Zeitchrift für Analysis und ihre Anwendungen (2005) 24 (375 - 388))

Abstract

In this note we prove that a harmonic function u on the unit ball B ⊂ ℝn belongs to the harmonic mixed norm space Asp,q (B), when p, q ∈ (0, ∞] and s > 0, if and only if all weighted tangential derivatives of order k (with positive orders of derivatives) belong to the related weighted Lebesgue mixed norm space sp'q(B). Our proof of the result for the case q ∈(0, 1) and k is odd, corrects the corresponding one in the paper: G. Ren and U. Kähler, Hardy-Littlewood inequalities and Qp-spaces, Z. Anal. Anwendungen 24 (2005), 375 - 388.