Geodesic
On a Class of Functionals on a Weighted First-Order Sobolev Space on the Real Line
Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 236-250

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Let $g$ be a Lebesgue measurable function on an interval $I\subset \mathbb R$. We find conditions on $g$ under which the mapping $f\mapsto \int _I g(x)(Df)(x)\,dx$ 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 $[W_{p,p}^1(I)]^*$. 
@article{TRSPY_2021_312_a13,
     author = {D. V. Prokhorov},
     title = {On a {Class} of {Functionals} on a {Weighted} {First-Order} {Sobolev} {Space} on the {Real} {Line}},
     journal = {Informatics and Automation},
     pages = {236--250},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a13/}
}
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D. V. Prokhorov. On a Class of Functionals on a Weighted First-Order Sobolev Space on the Real Line. Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 236-250. http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a13/