Taylor's inequalities in Orlicz–Sobolev type spaces

Federico Dario Kovac and Fabián Eduardo Levis

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1190-1203

Abstract: In this paper, we obtain inequalities involving the Taylor polynomial and weak derivatives of a function in an Orlicz–Sobolev type space. Moreover, we show that any such function can be expanded in a finite Taylor series almost everywhere. As a consequence, we prove that the coefficients of any extended best polynomial LΦ$L^\Phi$‐approximation of a function on a ball almost everywhere converge to the weak derivatives of such a function when the radius tends to 0. Lastly, we get a mean convergence result of such coefficients.

Date: 2023
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https://doi.org/10.1002/mana.202100135

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