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We study the uniformly bounded orthonormal systemU of functions u ( ) n (x)= ( ) n (cos x)(sin x) , x ∈ [0, ], where { ( ) n }∞n=0 ( > 0) is the normalized system of ultraspherical polynomials.We investigate some approximation properties of the systemU and we show that these properties are similar to one’s of the trigonometric system. First, we obtain(More)
We study the Lorentz spaces L p,s (R, µ) in the range 1 < p < s ≤ ∞, for which the standard functional ||f || p,s = ∞ 0 (t 1/p f * (t)) s dt t 1/s is only a quasi-norm. We find the optimal constant in the triangle inequality for this quasi-norm, which leads us to consider the following decomposition norm: ||f || (p,s) = inf k ||f k || p,s , where the(More)
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