On moduli of smoothness with Jacobi weights
We introduce the moduli of smoothness with Jacobi weights $(1 x)\alpha (1+x)\beta$ for functions in the Jacobi weighted spaces $L_p[ 1, 1],\; 0 < p \leq \infty $. These moduli are used to characterize the smoothness of (the derivatives of) functions in the weighted spaces $L_p$. If $1 \leq...
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| Date: | 2018 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1563 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We introduce the moduli of smoothness with Jacobi weights $(1 x)\alpha (1+x)\beta$ for functions in the Jacobi weighted spaces
$L_p[ 1, 1],\; 0 < p \leq \infty $. These moduli are used to characterize the smoothness of (the derivatives of) functions in the
weighted spaces $L_p$. If $1 \leq p \leq \infty$, then these moduli are equivalent to certain weighted $K$-functionals (and so they are
equivalent to certain weighted Ditzian – Totik moduli of smoothness for these $p$), while for $0 < p < 1$ they are equivalent
to certain “Realization functionals”. |
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