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

Let (,  d ,  μ ) be a space of homogeneous type, in the sense of Coifman and Weiss, with the upper dimension  ω . Assume that η ∈(0, 1) is the smoothness index of the wavelets on  constructed by Auscher and Hytönen. In this article, via grand maximal functions, the authors introduce the Hardy–Lorentz spacesH   *   p  ,  q(    )H_*^{p,q}\left( \mathcal{X} \right)with the optimal rangep  ∈   (    ω   ω  +  η    ,  ∞   )p \in \left( {{\omega \over {\omega + \eta }},\infty } \right)and  q ∈  (0, ∞]. When andp  ∈  (   ω   ω  +  η    ,  1  ]p \in ({\omega \over {\omega + \eta }},1]q ∈  (0, ∞], the authors establish its real-variable characterizations, respectively, in terms of radial maximal functions, non-tangential maximal functions, atoms, molecules, and various Littlewood–Paley functions. The authors also obtain its finite atomic characterization. As applications, the authors establish a real interpolation theorem on Hardy–Lorentz spaces, and also obtain the boundedness of Calderón–Zygmund operators on them including the critical cases. The novelty of this article lies in getting rid of the reverse doubling assumption of  μ  by fully using the geometrical properties of  expressed via its dyadic reference points and dyadic cubes and, moreover, the results in the case  q ∈  (0, 1) of this article are also new even when  satisfies the reverse doubling condition.

analysis and geometry in metric spaces

Real-Variable Characterizations of Hardy–Lorentz Spaces on Spaces of Homogeneous Type with Applications to Real Interpolation and Boundedness of Calderón–Zygmund Operators