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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 1, Pages 79–100 (Mi izv736)  

On necessary conditions for Fourier multipliers of weak type

A. V. Rozhdestvenskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain necessary conditions for a bounded function $\varphi$ to be a Fourier multiplier of weak type $(\psi(L)(G),\psi(L)(G))$, where $G=\mathbb R^d$ or $G=\mathbb T^d$, provided that the Young function $\psi(t)$ grows slower than $t\ln^{1/2}t$ as $t$ tends to infinity.

DOI: https://doi.org/10.4213/im736

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English version:
Izvestiya: Mathematics, 2007, 71:1, 75–95

Bibliographic databases:

UDC: 517.51
MSC: 42B15
Received: 27.12.2005

Citation: A. V. Rozhdestvenskii, “On necessary conditions for Fourier multipliers of weak type”, Izv. RAN. Ser. Mat., 71:1 (2007), 79–100; Izv. Math., 71:1 (2007), 75–95

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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