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Linear and bilinear multiplier operators for the Dunkl transform. (English) Zbl 1209.42006
The paper treats the problem of ${L}^{p}$ estimates for linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case. Using Hörmander’s technique and an explicit formula for the Dunkl translation operator, an analogue of the celebrated Hörmander multiplier theorem is proved in the Dunkl setting. In the bilinear case a strategy of Coifman and Meyer is applied to receive an ${L}^{p}$ estimate for the bilinear multiplier operators.
##### MSC:
 42B15 Multipliers, several variables 42B20 Singular and oscillatory integrals, several variables 46F12 Integral transforms in distribution spaces
##### References:
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