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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerrefunctions which are eigenfunctions of the differential operator Lf=-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomicHardy space H^1_{at}(X), which is a subspace of L^1((0,infty), x^alpha dx).Then we prove that the space H^1_{at}(X) is also characterized by the Riesztransform Rf=\sqrt{\pi}\frac{d}{dx}L^{-1/2}f in the sense that f\in H^1_{at}(X)if and only if f,Rf \in L^1((0,infty),x^alpha dx).

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions