3 years ago

On moduli of smoothness with Jacobi weights.

Kirill A.kopotun, Dany Leviatan, Igor A. Shevchuk

The main purpose of this paper is to introduce moduli of smoothness with Jacobi weights $(1-x)^\alpha(1+x)^\beta$ for functions in the Jacobi weighted $L_p[-1,1]$, $0<p\le \infty$, spaces. These moduli are used to characterize the smoothness of (the derivatives of) functions in the weighted $L_p$ spaces. If $1\le p\le\infty$, then these moduli are equivalent to certain weighted $K$-functionals (and so they are equivalent to certain weighted Ditzian-Totik moduli of smoothness for these $p$), while for $0<p<1$ they are equivalent to certain "Realization functionals".

Publisher URL: http://arxiv.org/abs/1709.00705

DOI: arXiv:1709.00705v2

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