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

The article examines isotropic Nikolskii and Besov spaces with norms definedusing $L_p$-averaged modulus of continuity of functions of appropriate order,instead of modulus of continuity of known order for fixed-order partialderivative functions. The author builds continuous linear mappings of suchspaces of functions defined in domains of $(1,\ldots,1)$-type (in a broadsense) to ordinary isotropic Nikolskii and Besov spaces in $ \mathbb R^d $ thatare function extension operators, thus incurring coincidence of both kinds ofspaces in the said domains. It is established that every bounded domain in $\mathbb R^d $ with a Lipschitzian boundary is a $(1,\ldots,1)$-type domain (ina broad sense). The article also provides weak asymptotics of approximationcharacteristics related to the problem of reconstruction of functions withtheir derivatives from function values at a given number of points, theS.B.Stechkin's problem for differential operator, and the problem of widthasymptotics for isotropic Nikolskii-Besov classes in those domains.

Extending functions from isotropic Nikolskii-Besov spaces and their approximating with derivatives