论文标题
终点弱的Schatten类估计和痕量公式用于Riesz的换向器在Heisenberg组上使用乘数转换
Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups
论文作者
论文摘要
沿Rochberg-Semmes，Lord-McDonald-Sukochev-Zanin和Fan-Lacey-Li的换向价值估计，我们建立了Riesz换向器的终点弱Schatten类估算，该估算值是通过Heisenberg of Heisenberg of jeisenberg of jeisenberg of jeisenbole sobole sobole sobole norm norm symbole $ f $ f $ f $ f $ f $ f $ f。我们利用的新工具是在Heisenberg组上构建一个奇异的痕量公式，该公式与使用双运算符积分一起，使我们能够绕过使用傅立叶分析的使用，并为一般分层谎言组中类似的换向器的奇异值估计提供了坚实的基础。
Along the line of singular value estimates for commutators by Rochberg-Semmes, Lord-McDonald-Sukochev-Zanin and Fan-Lacey-Li, we establish the endpoint weak Schatten class estimate for commutators of Riesz transforms with multiplication operator $M_f$ on Heisenberg groups via homogeneous Sobolev norm of the symbol $f$. The new tool we exploit is the construction of a singular trace formula on Heisenberg groups, which, together with the use of double operator integrals, allows us to bypass the use of Fourier analysis and provides a solid foundation to investigate the singular values estimates for similar commutators in general stratified Lie groups.
