TY - JOUR
T1 - On the Moduli of Smoothness with Jacobi Weights
AU - Kopotun, K. A.
AU - Leviatan, D.
AU - Shevchuk, I. A.
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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 ≤ p ≤ 1, 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.”.
AB - 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 ≤ p ≤ 1, 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.”.
UR - https://www.scopus.com/pages/publications/85053779422
U2 - 10.1007/s11253-018-1509-9
DO - 10.1007/s11253-018-1509-9
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AN - SCOPUS:85053779422
SN - 0041-5995
VL - 70
SP - 437
EP - 466
JO - Ukrainian Mathematical Journal
JF - Ukrainian Mathematical Journal
IS - 3
ER -