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

This paper is devoted to strict $K$- monotonicity and $K$-order continuity insymmetric spaces. Using the local approach to the geometric structure in asymmetric space $E$ we investigate a connection between strict $K$-monotonicityand global convergence in measure of a sequence of the maximal functions. Next,we solve an essential problem whether an existence of a point of $K$-ordercontinuity in a symmetric space $E$ on $[0,\infty)$ implies that the embedding$E\hookrightarrow{L^1}[0,\infty)$ does not hold. We finish this article with acomplete characterization of $K$-order continuity in a symmetric space $E$ thatis written using a notion of order continuity under some assumptions on thefundamental function of $E$.

Strict $K$-monotonicity and $K$-order continuity in symmetric spaces