In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ε centered at 0 on the upper half space Rd-1× ]0,+∞[. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p...
In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.
2000 Mathematics Subject Classification: 44A15, 44A35, 46E30
In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space.
* Supported by 04/UR/15-02.
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