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arXiv · 1408.2018

New moduli of smoothness

K. A. Kopotun·D. Leviatan·I. A. Shevchuk
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Abstract

In this paper, we discuss various properties of the new modulus of smoothness \[ \omega^\varphi_{k,r}(f^{(r)},t)_p := \sup_{0 < h\leq t}\|\mathcal W^r_{kh}(\cdot) \Delta_{h\varphi(\cdot)}^k (f^{(r)},\cdot)\|_{L_p[-1,1]}, \] where $\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.

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K. A. Kopotun, D. Leviatan, I. A. Shevchuk. 2014-08-09. New moduli of smoothness. https://arxiv.org/abs/1408.2018

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