Abstract
In this paper we obtain Ul’yanov type inequalities for fractional moduli of smoothness/K-functionals for the limit value parameters: p=1 or q=∞. Needed versions of Nikol’skii type inequalities for trigonometric polynomials are given. We show that these estimates are sharp. Corresponding embedding theorems for the Lipschitz spaces are investigated.
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Communicated by Paul Butzer.
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Tikhonov, S. Weak Type Inequalities for Moduli of Smoothness: The Case of Limit Value Parameters. J Fourier Anal Appl 16, 590–608 (2010). https://doi.org/10.1007/s00041-009-9101-1
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DOI: https://doi.org/10.1007/s00041-009-9101-1