Ukrainian Mathematical Journal

, Volume 70, Issue 3, pp 437–466

# On the Moduli of Smoothness with Jacobi Weights

• K. A. Kopotun
• D. Leviatan
• I. A. Shevchuk
Article

We introduce the moduli of smoothness with Jacobi weights (1 − x)𝛼(1 + x)β for functions in the Jacobi weighted spaces Lp[1, 1], 0 < p. These moduli are used to characterize the smoothness of (the derivatives of) functions in the weighted spaces Lp . If 1 ≤ p1, then these moduli are equivalent to certain weighted K-functionals (and, hence, they are equivalent to certain weighted Ditzian–Totik moduli of smoothness for these p), while for 0 < p < 1 they are equivalent to certain “realization functionals.”

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## Authors and Affiliations

• K. A. Kopotun
• 1
• D. Leviatan
• 2
• I. A. Shevchuk
• 3