Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms
Abstract We study sharp weak-type inequalities for a wide class of Fourier multipliers resulting from modulation of the jumps of Lévy processes. In particular, we obtain optimal estimates for second-order Riesz transforms, which lead to interesting a priori bounds for smooth functions on ℝd. The proofs rest on probabilistic methods: …