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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we prove higher order Poincar\'e inequalities involving radialderivatives namely,  \begin{equation*}  \int_{\mathbb{H}^{N}} |\nabla_{r,\mathbb{H}^{N}}^{k} u|^2 \, {\rmd}v_{\mathbb{H}^{N}} \geq \bigg(\frac{N-1}{2}\bigg)^{2(k-l)}\int_{\mathbb{H}^{N}} |\nabla_{r,\mathbb{H}^{N}}^{l} u|^2 \, {\rmd}v_{\mathbb{H}^{N}} \ \ \text{ for all } u\in H^k(\mathbb{H}^{N}),  \end{equation*} where underlying space is $N$-dimensional hyperbolic space$\mathbb{H}^{N}$, $0\leq l<k$ are integers and the constant$\big(\frac{N-1}{2}\big)^{2(k-l)}$ is sharp. Furthermore we improve the aboveinequalities by adding Hardy-type remainder terms and the sharpness of someconstants is also discussed.

On Higher order Poincar\'e Inequalities with radial derivatives and Hardy improvements on the hyperbolic space