Geodesic
On the Density of Compactly Supported Functions in a Space with Multiweighted Derivatives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 188-202

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We define a space with multiweighted derivatives on the half-axis. A multiweighted derivative of a function is an operation under which each subsequent derivative is taken of the function multiplied by some weight function. All weight functions involved in the definition of a multiweighted derivative are assumed to be sufficiently smooth; therefore, the set of compactly supported infinitely smooth functions belongs to the space with multiweighted derivatives, and the closure of this set in the norm of the space is a subspace of the latter. We study the mutual relation between these spaces depending on the integral behavior of the weight functions in the neighborhood of zero and infinity.
Keywords: weight function, multiweighted derivative, space with multiweighted derivatives, closure of the set of compactly supported functions, density. 
@article{TM_2021_312_a9,
     author = {A. A. Kalybay and Zh. A. Keulimzhayeva and R. Oinarov},
     title = {On the {Density} of {Compactly} {Supported} {Functions} in a {Space} with {Multiweighted} {Derivatives}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {188--202},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a9/}
}
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A. A. Kalybay; Zh. A. Keulimzhayeva; R. Oinarov. On the Density of Compactly Supported Functions in a Space with Multiweighted Derivatives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 188-202. http://geodesic.mathdoc.fr/item/TM_2021_312_a9/