- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:42
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
10
1994
3
On singular integrals of Calderón-type in $\mathbb R^n$, and BMO
Dorina
Mitrea
University of Missouri, COLUMBIA, UNITED STATES
We prove $L^p$ (and weighted $L^p$) bounds for singular integrals of the form $$\rm p.v. \int_{\mathbb R^n} E \lgroup \frac{A(x)–A(y)}{|x–y} \rgroup \frac{\Omega(x–y)}{|x–y|^n} f(y)dy,$$ where $E(t) =$ cos $t$ if $\Omega$ is odd, and $E(t) =$ sin $t$ if $\Omega$ is even, and where $\bigtriangledown A \in$ BMO. Even in the case that $\Omega$ is smooth, the theory of singular integrals with "rough" kernels plays a key role in the proof. By standard techniques, the trigonometric function $E$ can then be replaced by a large class of smooth functions $F$. Some related operators are also considered. As a further application, we prove a compactness result for certain layer potentials.
General
467
505
10.4171/RMI/159
http://www.ems-ph.org/doi/10.4171/RMI/159