EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 96[110], pp. 169–180 (2014)

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K. A. Kopotun, D. Leviatan, and I. A. Shevchuk

Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada; Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel and Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

Abstract: We discuss various properties of the new modulus of smoothness $$ \omega^\varphi_{k,r}(f^{(r)},t)_p:= \sup_{0<h\leq t}\|\mathcal W^r_{kh}(\cdot)\Delta_{h\varphi(\cdot)}^k (f^{(r)},\cdot)\|_{\Lp[-1,1]}, $$ where $\varphi(x):=\sqrt{1-x^2}$ and $\mathcal W_\delta(x)=\bigl((1-x-\delta\varphi(x)/2)(1+x-\delta\varphi(x)/2)\bigr)^{1/2}$. Related moduli with more general weights are also considered.

Classification (MSC2000): 41A17; 41A10, 42A10, 41A25, 41A27

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Electronic fulltext finalized on: 30 Oct 2014. This page was last modified: 24 Nov 2014.

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