jackson inequality
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2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kai-Cheng Wang

AbstractAlthough wavelet decompositions of functions in Besov spaces have been extensively investigated, those involved with mild decay bases are relatively unexplored. In this paper, we study wavelet bases of Besov spaces and the relation between norms and wavelet coefficients. We establish the $l^{p}$ l p -stability as a measure of how effectively the Besov norm of a function is evaluated by its wavelet coefficients and the $L^{p}$ L p -completeness of wavelet bases. We also discuss wavelets with decay conditions and establish the Jackson inequality.



2020 ◽  
Vol 20 (3) ◽  
pp. 441-451
Author(s):  
Horst Alzer ◽  
Man Kam Kwong
Keyword(s):  


2019 ◽  
Vol 56 (4) ◽  
pp. 500-509
Author(s):  
Horst Alzer ◽  
Man Kam Kwong

Abstract We prove: For all natural numbers n and real numbers x ∈ [0, π] we have . The sign of equality holds if and only if n = 2 and x = 4π/5.



2019 ◽  
Vol 105 (5-6) ◽  
pp. 657-673
Author(s):  
D. V. Gorbachev ◽  
V. I. Ivanov


2015 ◽  
Vol 288 (S1) ◽  
pp. 88-98
Author(s):  
V. I. Ivanov ◽  
Ha Thi Minh Hue


2015 ◽  
Vol 35 (2) ◽  
pp. 375-382
Author(s):  
Yi GU ◽  
Yongping LIU
Keyword(s):  


2014 ◽  
Vol 96 (5-6) ◽  
pp. 904-913 ◽  
Author(s):  
D. V. Gorbachev ◽  
V. I. Ivanov ◽  
R. A. Veprintsev


2014 ◽  
Vol 284 (S1) ◽  
pp. 41-58 ◽  
Author(s):  
A. G. Babenko ◽  
N. V. Dolmatova ◽  
Yu. V. Kryakin


2013 ◽  
Vol 21 ◽  
pp. 3
Author(s):  
T.A. Agoshkova

In the space $L_{\psi}[-1;1]$ of non-periodic functions with metric $\rho(f,0)_{\psi} = \int\limits_{-1}^1 \psi(|f(x)|)dx$, where $\psi$ is a function of the type of modulus of continuity, we study Jackson inequality for modulus of continuity of $k$-th order in the case of approximation by algebraic polynomials. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function $\psi$ is not equal to zero.



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