... Ω ∈L(logL)1/2(Sn−1)[2]. Moreover, we showed that if the condition Ω ∈ L(logL)1/2(Sn−1)isreplaced by any condition in the form Ω∈ L(logL)r(Sn−1)forsomer<1/2, then ᏹΩmight fail ... Ωq1−1/4q.(2.11)Therefore, by (2.7), (2.11), and [12, (3.11)], we obtainJk,Ω(ξ) ≤ 2γk,Ω/4qΩ2qqCloge + Ωq1−1/4q. (2.12)Ahmad Al-Salman 7 for some ε>0andforall2≤ p<∞,and ... Lp for all p ≥ 2[3]. Moreover, we showed that the condition Ω ∈B0,−1/2s(Sn−1), s>1 is nearly optimal in the sense that the exponent −1/2 cannot be re-placed by any smaller number for...