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On a Class of Functionals on a Weighted First-Order Sobolev Space on the Real Line
Proceedings of the Steklov Institute of Mathematics ( IF 0.4 ) Pub Date : 2021-04-22 , DOI: 10.1134/s0081543821010144
D. V. Prokhorov

Abstract

Let \(g\) be a Lebesgue measurable function on an interval \(I\subset\mathbb R\). We find conditions on \(g\) under which the mapping \(f\mapsto \intop_I g(x)(Df)(x)\,dx\) is a continuous linear functional on a weighted first-order Sobolev space \(W_{p,p}^1(I)\); we also obtain estimates for the norm of this functional in \([W_{p,p}^1(I)]^*\).



中文翻译:

关于实线上加权一阶Sobolev空间上的一类泛函

摘要

\(g \)为区间\(I \ subset \ mathbb R \)上的Lebesgue可测量函数。我们在\(g \)上找到条件,在该条件下映射\(f \ mapsto \ intop_I g(x)(Df)(x)\,dx \)是加权一阶Sobolev空间\ { W_ {p,p} ^ 1(I)\) ; 我们还在\([W_ {p,p} ^ 1(I)] ^ * \)中获得此函数范数的估计。

更新日期:2021-04-23
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