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12 161 172 Csáki, E. and Csörgő, M. , Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab

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of continuity, Ann. Probab. , 20 (1992), no. 2, 1031–1052. MR 93c :60055 Csörgő M. Inequalities for increments of stochastic processes and moduli of continuity

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Series 1959 Aljanćić, S. , On the integral moduli of continuity in L p (1 < p < ∞) of Fourier

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References [1] Aljančić , S. 1966 On the integral moduli of continuity in L p (1< p <∞) of Fourier series with monotone coefficients

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Abstract  

We consider the Walsh orthonormal system on the interval [0, 1) in the Paley enumeration and the Walsh-Fourier coefficients

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(n), n ∈ ℕ, of functions fL p for some 1 < p ≤ 2. Our aim is to find best possible sufficient conditions for the finiteness of the series Σn=1 a n|
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(n)|r, where {a n} is a given sequence of nonnegative real numbers satisfying a mild assumption and 0 < r < 2. These sufficient conditions are in terms of (either global or local) dyadic moduli of continuity of f. The sufficient conditions presented in the monograph [2] are special cases of our ones.

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49 54 Adell, J. A. And DE LA Cal, J., Preservation of moduli of continuity for Bernsteintype operators, Approximation, probability, and related fields (Santa Barbara, CA, 1993

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CSÁKI, E. and CSORGÖ, M., Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab. 20 (1992), 1031-1052. MR 93c :60055 Inequalities for increments of stochastic processes and moduli of

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Anastassion, G. A. and Gál, S. G. , Approximation theory, Moduli of Continuity and Global Gmoothness Reservation , Birkhäuser, Boston, Basel, Berlin, 1999

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12 161 172 Csáki, E. and Csörgő, M. , Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab

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Math. Z. 28 612 – 634 10.1007/BF01181186 . [6] Kolyada , V. I. 1988 On relations between moduli of continuity in different

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