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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 245–255 (Mi mz8045)  

A weighted estimate of best approximations in $L_2(\Omega)$

Yu. K. Dem'yanovich

Leningrad State University

Abstract: The best approximation $\widetilde f$ [in the space $L_2(\Omega)$] of a function $f$, satisfying a Lipschitz condition with exponent $\alpha$, $0\le\alpha\le1$, with the aid of certain spaces of local functions, dependent on a parameter $h$, is discussed. We obtain the estimate
$$ \|f-\widetilde f\|_\beta\le\widetilde C(f)h^{\min\{\alpha,\beta\}}, $$
where
$$ \|u\|_\beta=\max_{x\in\overline\Omega}|r^\beta u(x)|,\quad\beta\ge0\quad u\in C(\overline\Omega) $$
and $r=r(x)$ is the distance of the point $x$ from the boundary of the domain $\Omega$.

Full text: PDF file (574 kB)

English version:
Mathematical Notes, 1977, 22:2, 627–633

Bibliographic databases:

UDC: 517.5
Received: 12.01.1976

Citation: Yu. K. Dem'yanovich, “A weighted estimate of best approximations in $L_2(\Omega)$”, Mat. Zametki, 22:2 (1977), 245–255; Math. Notes, 22:2 (1977), 627–633

Citation in format AMSBIB
\Bibitem{Dem77}
\by Yu.~K.~Dem'yanovich
\paper A~weighted estimate of best approximations in $L_2(\Omega)$
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 245--255
\mathnet{http://mi.mathnet.ru/mz8045}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487189}
\zmath{https://zbmath.org/?q=an:0431.41039}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 627--633
\crossref{https://doi.org/10.1007/BF01780972}


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