Geodesic
A sharp correction theorem
Studia Mathematica, Tome 113 (1995) no. 2, pp. 177-196

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Under certain conditions on a function space X, it is proved that for every $L^∞$-function f with $∥f∥_{∞} ≤ 1$ one can find a function φ, 0 ≤ φ ≤ 1, such that φf ∈ X, $mes{φ ≠ 1} ≤ ɛ∥f∥_1$ and $∥φf∥_X ≤ const(1 + log ɛ^{-1})$. For X one can take, e.g., the space of functions with uniformly bounded Fourier sums, or the space of $L^∞$-functions on $ℝ^n$ whose convolutions with a fixed finite collection of Calderón-Zygmund kernels are also bounded.
DOI : 10.4064/sm-113-2-177-196

S. V. Kisliakov 1

1 
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S. V. Kisliakov. A sharp correction theorem. Studia Mathematica, Tome 113 (1995) no. 2, pp. 177-196. doi: 10.4064/sm-113-2-177-196

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