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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We use precise asymptotic expansions for Jacobi functions$\phi^{(\alpha,\beta)}_\lambda$ parameters $\alpha$, $\beta$ satisfying$\alpha>1/2$, $\alpha>\beta>-1/2$, to generalizing classical H\"ormander-typemultiplier theorem for the spherical transform on a rank one Riemanniansymmetric space (by Clerc/Stein and Stanton/Tomas) to the framework of Jacobianalysis. In particular, multiplier results for the spherical transform onDamek--Ricci spaces are subsumed by this approach, and it yields multiplierresults for the hypergeometric `Heckman--Opdam transform' associated with arank one root system. We obtain near-optimal $L^p-L^q$ estimates for theintegral operator associated with the convolution kernel$m_a:\lambda\mapsto(\lambda^2+\rho^2)^{-a/2}$, $a>0$.

$L^p$-results for fractional integration and multipliers for the Jacobi transform