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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