论文标题
Björk-Sjölin条件强烈的奇异卷积操作员在分级谎言组上
Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups
论文作者
论文摘要
在这项工作中，我们将强烈奇异卷积操作员的$ l^1 $-Björk-Sjölin理论扩展到任意分级的谎言组。我们的标准是根据操作员内核的Björk和Sjölin引起的振荡Hörmander条件提出的，其组傅立叶变换的衰减是根据任意岩石运营商的无限表示来衡量的。在欧几里得空间的情况下，Björk和Sjölin的历史结果被重新概括。
In this work we extend the $L^1$-Björk-Sjölin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillating Hörmander condition due to Björk and Sjölin of the kernel of the operator, and the decay of its group Fourier transform is measured in terms of the infinitesimal representation of an arbitrary Rockland operator. The historical result by Björk and Sjölin is re-obtained in the case of the Euclidean space.
