Abstract：In this paper， the oscillation of the Poisson semigroup associated with parabolic Bessel operator L＝?t－Δx－x2(1/4－μ2)(μ〉－1) is considered. The oscillation operator O(PLτ) is bounded from Lp(?2)(1〈p〈∞) into itself， from L1(?2)into weak－L1(?2)， and bounded from Lc(∞)(?2) into BMO(?2) is proved by the parabolic semigroup method and Calderón-Zygmund theory. In the case p＝∞， it is showed that the range of the image of the oscillation O(PLτ) is strictly smaller than the range of a general singular operator in some sense.
2023, Vol. 57 
