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This article deals with some special cases which are extension of the strong summability of Fourier series with constant factor. We obtain a new equivalent form of inequalities A 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) φ (z) 2 dρ r/2 dθ ≤ B 2π 0 φ(e iθ) r dθ, (1) 2π 0 1 0 (1 − ρ) q−1 φ (z) q dρ r/q dθ ≤ C 2π 0 φ(e iθ) r dθ, (2) D 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0(More)
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