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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

uppose that d ≥ 1 is an integer, $${\alpha \in (0,d)}$$α∈(0,d) is a fixed parameter and let Iα be the fractional integral operator associated with d-dimensional Walsh–Fourier series on [0, 1)d. The paper contains the proof of the sharp weak-type estimate$$||I_\alpha(f)||_{L^{d/(d-\alpha),\infty}([0,1)^d)}\leq\frac{2^d-1}{(2^{d-\alpha}-1)(2^\alpha-1)}||f||_{L^1([0,1)^d)}.$$||Iα(f)||Ld/(d-α),∞([0,1)d)≤2d-1(2d-α-1)(2α-1)||f||L1([0,1)d).The proof rests on Bellman-function-type method: the above estimate is deduced from the existence of a certain family of special functions.

Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh–Fourier Series