Some sharp estimates for the second continuity modulus for periodic functions and for functions extended from a segment

1998 ◽  
Vol 92 (1) ◽  
pp. 3560-3572
Author(s):  
O. L. Vinogradov
Keyword(s):  
Periodic Functions ◽  
Continuity Modulus ◽  
Sharp Estimates

scholarly journals Some sharp inequalities for approximations of periodic functions in $L_1$ space

1987 ◽  
pp. 4
Author(s):  
V.F. Babenko
Keyword(s):  
Periodic Functions ◽  
Piecewise Constant ◽  
Sharp Estimates ◽  
Alpha Beta

We provide sharp estimates of Jackson's inequalities type for the best $(\alpha, \beta)$-approximations in the space $L_1$ of periodic functions that are representable as the convolution of the kernel $K$ that does not increase the number of sign alternations with functions $\varphi \in C$, by means of convolutions of the kernel $K$ with the functions that are piecewise-constant in the intervals $\bigl( \frac{l \pi}{n}, \frac{(l+1)\pi}{n} \bigr)$.

On the Absolute Convergence of Fourier Series

1997 ◽  
Vol 4 (4) ◽  
pp. 333-340
Author(s):  
T. Karchava
Keyword(s):  
Fourier Series ◽  
Finite Number ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Sufficient Conditions ◽  
Trigonometric Fourier Series ◽  
Periodic Functions ◽  
Continuity Modulus ◽  
The Absolute ◽  
Necessary And Sufficient

Abstract The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2π-periodic functions which in [0, 2π] have a finite number of intervals of convexity, and whose 𝑛th Fourier coefficients are O(ω(1/𝑛; 𝑓)/𝑛), where ω(δ; 𝑓) is the continuity modulus of the function 𝑓.

scholarly journals Functions of Boundedkthp-Variation and Continuity Modulus

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Odalis Mejía ◽  
Pilar Silvestre
Keyword(s):  
Sobolev Space ◽  
Modulus Of Smoothness ◽  
Continuity Modulus ◽  
Sharp Estimates ◽  
Class Of Functions

A scale of spaces exists connecting the class of functions of boundedkthp-variation in the sense of Riesz-Merentes with the Sobolev space of functions withp-integrablekth derivative. This scale is generated by the generalized functionals of Merentes type. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of smoothness of orderk-1/p.

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