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Mixed Moduli of Smoothness in $L_p$, $1<p<infty$ | | M. K. Potapov
; B. V. Simonov
; S. Yu. Tikhonov
; | | Date: |
11 Apr 2013 | | Abstract: | In this paper we survey recent developments over the last 25 years on the
mixed fractional moduli of smoothness of periodic functions from $L_p$,
$1<p<infty$. In particular, the paper includes monotonicity properties,
equivalence and realization results, sharp Jackson, Marchaud, and Ul’yanov
inequalities, interrelations between the moduli of smoothness, the Fourier
coefficients, and "angular" approximation. The sharpness of the results
presented is discussed. | | Source: | arXiv, 1304.3329 | | Services: | Forum | Review | PDF | Favorites | |
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