Displaying similar documents to “Almost everywhere convergence of Fourier integrals in Rn”

Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms

Adam Osękowski (2014)

Open Mathematics

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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: we deduce the above inequalities from the corresponding estimates for martingales. To obtain the lower bounds, we exploit the properties of laminates, important probability...