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 Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

We consider the fractional Laplacian with Hardy potential and study the scaleof homogeneous $L^p$ Sobolev spaces generated by this operator. Besidesgeneralized and reversed Hardy inequalities, the analysis relies on aH\"ormander multiplier theorem which is crucial to construct a basicLittlewood--Paley theory. The results extend those obtained recently in $L^2$but do not cover negative coupling constants in general due to the slow decayof the associated heat kernel.

On Scales of Sobolev spaces associated to generalized Hardy operators