Abstract
The smoothness spaces 𝓒 αp , introduced by DeVore and Sharpley in [5], coincide with the Sobolev spaces W αp for integer α and p > 1. Considering them as a natural extension of the Sobolev spaces for fractional α and values of p > 0, we compute the n-widths dn(U(𝓒 αp ), Lq) for a > N/p — N/q , 0 < p ≤ ∞, 1 ≤ q ≤ + ∞.
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DeVore, R.A., Sharpley, R.C., Riemenschneider, S.D. (1984). n-Widths for 𝓒 αp Spaces. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_21
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DOI: https://doi.org/10.1007/978-3-0348-5432-0_21
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