@MISC{Auscher08(0.2)‖∇g‖, author = {Pascal Auscher}, title = {(0.2) ‖∇g‖ ∞ ≤ Cα,}, year = {2008} }

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Abstract

We correct an inaccuracy in the proof of a result in [Aus1]. 2000 MSC: 42B20, 46E35 Key words: Calderón-Zygmund decomposition; Sobolev spaces. We recall the lemma. Lemma 0.1. Let n ≥ 1, 1 ≤ p ≤ ∞ and f ∈ D ′ (R n) be such that ‖∇f‖p < ∞. Let α> 0. Then, one can find a collection of cubes (Qi), functions g and bi such that (0.1) f = g + ∑ and the following properties hold: