Lp-gradient estimates for the commutators of the Kato square roots of second-order elliptic operators on Rn

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 575-594
• 页数: 20页
• 语种: 英文

摘要

Let L =-div(A▽) be a second-order divergent-form elliptic operator,where A is an accretive n × n matrix with bounded and measurable complex coefficients on Rn.Herein,we prove that the commutator [b,√L] of the Kato square root √/L and b with ▽b ∈ Ln(Rn) (n ＞ 2),is bounded from the homogenous Sobolev space (L)p1(Rn) to Lp(Rn) (p-(L) ＜p ＜ p+(L)).