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A recent result of Kateb asserts that f∈Bp,qs(ℝn) implies |f|μ∈Bp,qs(ℝn) as soon as the following three conditions hold: (1) 0≺s≺μ+(1/p), (2) f is bounded, (3) μ≻1. By means of counterexamples, we prove that those conditions are optimal

A sharpness result for powers of Besov functions