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Fourier multipliers associated with singular partial differential operators. (English) Zbl 1366.43003
The authors establish a Bernstein type inequality for the generalized translation associated with the Riemann-Liouville operator. This inequality permits them to prove the Hörmander-Mikhlin multiplier theorem for the Fourier transform associated with the Riemann-Liouville operator.

MSC:
43A32 Other transforms and operators of Fourier type
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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