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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:
42B15Multipliers, several variables
42B20Singular and oscillatory integrals, several variables
46F12Integral transforms in distribution spaces
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