Some Generalized Besov-Type Space $ B_{p\theta}^{\varphi}([0,1];H) $ with the Haar Basis

E Smailov

2022

Closed access Metadata (CSL-JSON)
DOI 10.1134/s0037446622060131
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

We introduce the generalized Besov-type space $ B_{p\theta}^{\varphi}([0,1];H) $ over the Haar basis. We give the two-sided estimate for the norm of functions of the space in terms of their Fourier–Haar coefficients. Also, we establish a criterion for the embedding $ B_{p\theta}^{\varphi}([0,1];H)\hookrightarrow L_{q\tau}[0,1] $ and some two-sided estimate for the approximation of $ B^{\varphi}_{p\theta}([0,1],H) $ in the metric of $ L_{q\tau}[0,1] $ , with $ 1\leq p<q<+\infty $ and $ {1\leq\tau<+\infty} $ .