English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The goal of this paper is to study operators of the form, \[ Tf(x)=\psi(x)\int f(\gamma_t(x))K(t)\: dt, \] where $\gamma$ is a real analyticfunction defined on a neighborhood of the origin in $(t,x)\in \R^N\times \R^n$,satisfying $\gamma_0(x)\equiv x$, $\psi$ is a cutoff function supported near$0\in \R^n$, and $K$ is a "multi-parameter singular kernel" supported near$0\in \R^N$. A main example is when $K$ is a "product kernel." We also studymaximal operators of the form, \[ \mathcal{M} f(x) =\psi(x)\sup_{0<\delta_1,..., \delta_N<<1} \int_{|t|<1} |f(\gamma_{\delta_1t_1,...,\delta_N t_N}(x))|\: dt. \] We show that $\mathcal{M}$ is bounded on$L^p$ ($1<p\leq \infty$). We give conditions on $\gamma$ under which $T$ isbounded on $L^p$ ($1<p<\infty$); these conditions hold automatically when $K$is a Calder\'on-Zygmund kernel. This is the final paper in a three part series.The first two papers consider the more general case when $\gamma$ is$C^\infty$.

Multi-parameter singular Radon transforms III: real analytic surfaces