A note on K-functional, Modulus of smoothness, Jackson theorem and Nikolskii-Stechkin inequality on Damek-Ricci spaces

2020/05/04 by Kumar, Vishvesh, Ruzhansky, Michael
#22E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 41A17

paper · doi:10.48550/arxiv.2005.01413

Abstract

In this paper we study approximation theorems for L²-space on Damek-Ricci spaces. We prove direct Jackson theorem of approximations for the modulus of smoothness defined using spherical mean operator on Damek-Ricci spaces. We also prove Nikolskii-Stechkin inequality. To prove these inequalities we use functions of bounded spectrum as a tool of approximation. Finally, as an application, we prove equivalence of the K-functional and modulus of smoothness for Damek-Ricci spaces.

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