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Maximal functions for Weinstein operator

100%

Abdelkefi C.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2020

tom 19

105-119

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 ≤+∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.

The class Bpfor weighted generalized Fourier transform inequalities

63%

Abdelkefi C., Rachdi M.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2015

tom 14

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.

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2 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2 Abdelkefi C.

1 Rachdi M.

1 2020

1 2015

Wyniki wyszukiwania

Maximal functions for Weinstein operator

The class Bpfor weighted generalized Fourier transform inequalities