Realization and characterization of modulus of smoothness in weighted Lebesgue spaces

R. Akgün

Algebra i analiz, Tome 26 (2014) no. 5, pp. 64-87.

Résumé

A characterization is obtained for the modulus of smoothness of fractional order in the Lebesgue spaces $L_\omega^p$, $1$, 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 $1$ and $\omega\in A_p$.

Détail

Keywords: fractional modulus of smoothness, realization, muckenhoupt weight, characterization, $K$-functional.

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