关于Calderon-Zygmund算子核的光滑性的讨论

On the Smoothness of the Kernels of C-Z Operators

对于一般的非卷积型Calderon -Zygmund算子 ,核满足Hormander条件能否保证L2 有界性 ,这是尚未解决的一个问题 .我们已在条件∑k1 2 ε1 (k) <∞下 ,证明了L2 有界 .∑k1 2 ε1 (k) <∞条件与Hormander条件有何关系 。

For general C-Z operators of non-convolution type,we showed that under the condition of ∑k 12 φ(k)<∞ ,T is bounded on L 2 .we also gived examples to show the condition of ∑k 12 φ(k)<∞ is independent of the Hormander condition .