Realization and characterization of modulus of smoothness in weighted Lebesgue spaces

Akgün, R.

doi:10.1090/spmj/1356

Realization and characterization of modulus of smoothness in weighted Lebesgue spaces
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by R. Akgün

St. Petersburg Math. J. 26 (2015), 741-756

DOI: https://doi.org/10.1090/spmj/1356

Published electronically: July 27, 2015

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Abstract:

A characterization is obtained for the modulus of smoothness in the Lebesgue spaces $L_{\omega }^{p}$, $1<p<\infty$, with weights $\omega$ satisfying the Muckenhoupt $A_{p}$ condition. Also, a realization result and the equivalence between the modulus of smoothness and the Peetre $K$-functional are proved in $L_{\omega }^{p}$ for $1<p<\infty$ and $\omega \in A_{p}$.

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