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

In this article, we study the regularity of the non-centered fractional maximal operator   $M_{\beta}$  . As the main result, we prove that there exists   $C(n,\beta)$   such that if   $q=n/(n-\beta)$   and   $f$   is  radial function , then   $\|DM_{\beta}f\|_{L^{q}({\mathbb{R}^n})}\leq C(n,\beta)\|Df\|_{L^{1}({\mathbb{R}^n})}$  . The corresponding result was previously known only if   $n=1$   or   $\beta=0$  . Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all   $f\in W^{1,1}({\mathbb{R}^n})$  .

The Variation of the Fractional Maximal Function of a Radial Function