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

Let $T_{\vec{b}}$ and $T_{\Pi b}$ be the commutators in the $j$-th entry anditerated commutators of the multilinear Calder\'{o}n-Zygmund operators,respectively. It was well-known that $T_{\vec{b}}$ and $T_{\Pi b}$ were not ofweak type $(1,1)$ and $(H^1, L^1)$, but they did satisfy certain endpoint$L\log L$ type estimates. In this paper, our aim is to give more natural sharpendpoint results. We show that $T_{\vec{b}}$ and $T_{\Pi b}$ are bounded fromproduct Hardy space $H^1\times\cdot\cdot\cdot\times H^1$ to weak$L^{\frac{1}{m},\infty}$ space, whenever the kernel satisfies a class of Dinitype condition. This was done by using a key lemma given by M. Christ, a verycomplex decomposition of the integrand domains and splitting and estimating thecommutators very carefully into several terms and cases.

Endpoint estimates for the commutators of multilinear Calder\'{o}n-Zygmund operators with Dini type kernels