On approximation by rational functions with prescribed numerator degree in Lp spaces

Author： Yu Dan Sheng   Zhou Song Ping  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.111, Iss.3, 2006-05, pp. : 221-236

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Abstract

It is proved that, if ]]>]]>]]>]]>]]>]]>]]>f(x)in L^p_{[-1,1]}$, $1< pki infty$, changes sign exactly $l$ times, then there exists a real rational function $r(x)in R_{n}^l$ such that ]]> {|f-r|}_{p}le C_{p,delta}{(l+1)}^2omega {(f,n^{-1})}_p, $$ which generalizes a result of Leviatan and Lubinsky in cite{4}. A weaker similar result in $L^1_{[-1,1]}$ is also established.

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