Mixed modulus of smoothness with Muckenhoupt weights and approximation by angle |
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| Authors: | Ramazan Akgün |
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| Affiliation: | Faculty of Arts and Sciences, Department of Mathematics, Balikesir University , Balikesir, Turkey |
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| Abstract: | Mixed modulus of smoothness in weighted Lebesgue spaces with Muckenhoupt weights are investigated. Using mixed modulus of smoothness we obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. Also we obtain equivalences between mixed modulus of smoothness and K-functional and realization functional. Fractional order modulus of smoothness is considered as well. |
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| Keywords: | Direct theorem inverse theorem Muckenhoupt weights modulus of smoothness |
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