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

NEW MODULI OF SMOOTHNESSK. A. Kopotun, D. Leviatan, and I. A. ShevchukDepartment 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, UkraineAbstract: 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 $\varphi(x):=\sqrt{1x^2}$ and $\mathcal W_\delta(x)=\bigl((1x\delta\varphi(x)/2)(1+x\delta\varphi(x)/2)\bigr)^{1/2}$. Related moduli with more general weights are also considered. Classification (MSC2000): 41A17; 41A10, 42A10, 41A25, 41A27 Full text of the article: (for faster download, first choose a mirror)
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