Open AccessInequalities of various metrics for the norms $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a,b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$ of differentiable functions on the real domain
Author(s) -
В. А. Кофанов
Publication year - 2018
Publication title -
vìsnik dnìpropetrovsʹkogo unìversitetu. serìâ matematika
Language(s) - English
Resource type - Journals
eISSN - 2518-7996
pISSN - 2312-9557
DOI - 10.15421/241806
Subject(s) - differentiable function , mathematics , real line , trigonometry , trigonometric functions , line (geometry) , delta , pure mathematics , combinatorics , mathematical analysis , physics , geometry , astronomy
We prove sharp inequalities of various metrics for the norms $$$\| x \|_{p, \delta}$$$ of differentiable functions defined on the real line, trigonometric polynomials and periodic splines.