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

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fourier multiplier; Singular integral; Martingale

Kategorie tematyczne

• 42B15: Multipliers
• 60G44: Martingales with continuous parameter
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1198-1213

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

Adam Osękowski

• University of Warsaw

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-014-0401-6