Logaritmic convolution condition for homogeneous Calderón-Zygmund kernel
University of Missouri
Homogeneous Calderón-Zygmund kernel is a convolution
kernel of the type
where
is an integrable function with mean zero on the unit sphere
.
It is well known that the
corresponding convolution operator is bounded on
if and only if
the convolution
![\begin{displaymath}
\int_{S^{n-1}} \Omega(\theta)\log \frac 1{\vert\xi \cdot \theta\vert} d\theta
\end{displaymath}](img5.png) |
(1) |
is essentially bounded. We provide an example that shows that on
,
,
the condition (
) is no longer sufficient.
2005-05-23