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Nikol'skii inequalities for Lorentz-Zygmund spaces

: Doktorski, Leo R. Ya; Gendler, Dmitrij


Boletin de la Sociedad Matemática Mexicana 25 (2019), No.3, pp.659-672
ISSN: 1405-213X (Print)
ISSN: 2296-4495 (Online)
Journal Article
Fraunhofer IOSB ()

Analogs of the Nikol’skii inequality in Lorentz–Zygmund spaces are obtained for functions of the form ∑nk=1ckφk, where {φk} is a finite orthonormal system in L2 bounded in L∞. No assumptions about smoothness of considered functions are required. Used technique relies only on the properties of Lorentz–Zygmund spaces and Fourier series map. In addition, real interpolation method is applied.