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Realization and characterization of modulus of smoothness in weighted Lebesgue spaces


Author: R. Akgün
Original publication: Algebra i Analiz, tom 26 (2014), nomer 5.
Journal: St. Petersburg Math. J. 26 (2015), 741-756
MSC (2010): Primary 26B35, 46E35
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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Additional 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

DOI: https://doi.org/10.1090/spmj/1356
Keywords: Fractional modulus of smoothness, realization, Muckenhoupt weight, characterization, $K$-functional
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.
Article copyright: © Copyright 2015 American Mathematical Society