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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We obtain several versions of the Hausdorff-Young and Hardy-Littlewoodinequalities for the $(k,a)$-generalized Fourier transform recentlyinvestigated at length by Ben Sa\"i d, Kobayashi, and {\O} rsted. We alsoobtain a number of weighted inequalities - in particular Pitt's inequality -that have application to uncertainty principles. Specifically we obtain severalanalogs of the Heisenberg-Pauli-Weyl principle for $L^p$-functions, localCowling-Price-type inequalities, Donoho-Stark-type inequalities and qualitativeextensions. We finally use the Hausdorff-Young inequality as a means to obtainentropic uncertainty inequalities.

Weighted inequalities and uncertainty principles for the $\boldsymbol{(k,a)}$-generalized Fourier transform