Let 픹 ⁿ be the unit ball and S ⁿ be the unit sphere in ℂ ⁿ, n ≥ 2. Let 0 < α < 1, and define a function f on [InlineMediaObject not available: see fulltext.] as follows: [Figure not available: see fulltext.] The main result of the paper is the following theorem: the function ζ ↦ |f(ζ)| on the unit sphere S ⁿ belongs to the Hölder class H ^α(S ⁿ), while the function f does not belong to the Hölder class [InlineMediaObject not available: see fulltext.] for any ε > 0.