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

Adam Osękowski

Open Mathematics, Tome 12 (2014), p. 1198-1213 / Harvested from The Polish Digital Mathematics Library

Résumé

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 measures on the space of matrices of dimension 2×2, and some transference-type arguments.

Détail

Publié le : 2014-01-01

Zbl 1290.42030

EUDML-ID : urn:eudml:doc:269645

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