Inequalities 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

V.A. Kofanov (Oles Honchar Dnipro National University), http://orcid.org/0000-0003-0392-2257

Abstract


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.

Keywords


inequalities of various metrics; trigonometric polynomials; splines

References


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DOI: https://dx.doi.org/10.15421/241806

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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557