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/

Zendy Plus

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

Zendy Tools

Zendy Open

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with apotential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with$\sigma\geq n/2$. The main aim of this paper is to provide necessary andsufficient conditions in terms of $T1$ criteria for a generalisedCalder\'on--Zygmund type operator with respect to $L$ to be bounded on Hardyspaces $H^p_L(\mathbb{R}^n)$ and on BMO type spacesBMO$_L^\alpha(\mathbb{R}^n)$ associated with $L$. As applications, we prove theboundedness for several singular integral operators associated to $L$. Ourapproach is flexible enough to prove the boundedness of the Riesz transformsrelated to $L$ with $n/2 \leq \sigma <n$ which were investigated in \cite{MSTZ}under the stronger condition $\sigma\geq n$. Thus our results not only recoverexisting results in \cite{MSTZ} but also contains new results in literature.

$T1$ criterions for generalised Calder\'on--Zygmund type operators on Hardy and BMO spaces associated to Schr\"odinger operators and applications