An Oscillating Integral in Ḃ0,11(Rn)

AbstractThis paper considers a convolution operator Tƒ = P.V. Ω * ƒ with Ω(x) = K(x)eih(x), where K(x) is a Calderón-Zygmund kernel and h(x) is a real-valued differentiable function satisfying (1.3). We prove that the operator T extends to a bounded operator in the Besov space Ḃ0,11(Rn) if and only if T is bounded in L2(Rn)