On One Generalized Translation and the Corresponding Inequality of Different Metrics
Vitalii Vladimirovich Arestov, M. V. Deikalova · Proceedings of the Steklov Institute of Mathematics · 2022
In this paper, we discuss the properties of the generalized translation operator generated by the system of functions $$\left\{\cos\left(\frac{(2k-1)\pi}{2}t\right)\right\}_{k=1}^{\infty}$$ in the spaces $$L^{p}(0,1)$$ , $$p\geq 1$$ . The translation operator is applied to the study of the Nikol’skii inequality between the uniform norm and the $$L^{p}$$ -norm of polynomials in this system.