Derivative Estimates of Iterated Spherical Average and Extension

• 作者: Meng WANG Jun Yan ZHAO
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（7）
• 页码范围: 1109-1130
• 页数: 22页
• 语种: 英文

摘要

In the paper,we study derivative estimates of the iterated spherical averages (At)N(f).We obtain the optimal range of exponents (α,N,p) to ensure the Lp boundedness of P((e)/(e)x)(A1)N(f)for 1 ≤ p ≤ ∞,where P is a homogeneous polynomial of degree α.The main theorem extends some known results.As an application,we obtain the smallest N such that (A1)N :Lp(Rn) → Lpα(Rn).