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 $\omega \in A_{p}$.References
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Bibliographic Information
- R. Akgün
- Affiliation: Department of Mathematics, Faculty of Arts and Sciences, Balikesir University, ÇağIş Yerleşkesi, 10145 Balikesir, Türkiye; Centre de Recerca Matemàtica (CRM), Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain
- Email: rakgun@balikesir.edu.tr
- Received by editor(s): October 7, 2013
- Published electronically: July 27, 2015
- Additional Notes: Partially supported by grant 2219 no. 2012-1-9246 of The Scientific and Technological Research Council of Turkey, TÜBITAK and MTM2011-27637.
- © Copyright 2015 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 741-756
- MSC (2010): Primary 26B35, 46E35
- DOI: https://doi.org/10.1090/spmj/1356
- MathSciNet review: 3442846