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

For a periodic function $f$ with bounded variation and integral zero on itsperiod interval, we show that $\sum_{k=1}^\infty c_k^2 (\log\log k)^\gamma<\infty$, $\gamma>4$ implies the almost everywhere convergence of$\sum_{k=1}^\infty c_k f(n_kx)$ for any increasing sequence $(n_k)$ ofintegers. We also construct an example showing that the previous condition isnot sufficient for $\gamma<2$. Finally we give an a.e. bound for the growth ofsums $\sum_{k=1}^N f(n_kx)$ differing from the corresponding optimal result fortrigonometric sums by a loglog factor.

On convergence and growth of sums $\sum c_k f(kx)$