On moduli of smoothness with Jacobi weights

  • K. A. Kopotun
  • D. Leviatan Tel Aviv Univ., Israel
  • I. A. Shevchuk

Abstract

We introduce the moduli of smoothness with Jacobi weights $(1 x)\alpha (1+x)\beta$ for functions in the Jacobi weighted spaces $L_p[ 1, 1],\; 0 < p \leq \infty $. These moduli are used to characterize the smoothness of (the derivatives of) functions in the weighted spaces $L_p$. If $1 \leq p \leq \infty$, 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”.
Published
25.03.2018
How to Cite
KopotunK. A., LeviatanD., and ShevchukI. A. “On Moduli of Smoothness With Jacobi Weights”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 3, Mar. 2018, pp. 379-03, http://umj.imath.kiev.ua/index.php/umj/article/view/1563.
Section
Research articles