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A dispersion inequality in the Hankel setting

Saifallah Ghobber (2018)

Czechoslovak Mathematical Journal

The aim of this paper is to prove a quantitative version of Shapiro's uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory.

BMO and commutators of martingale transforms

Svante Janson (1981)

Annales de l'institut Fourier

The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on L p , 1 < p < , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

Critical length for a Beurling type theorem

Michel Mehrenberger (2005)

Bollettino dell'Unione Matematica Italiana

In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.

Dunkl-Gabor transform and time-frequency concentration

Saifallah Ghobber (2015)

Czechoslovak Mathematical Journal

The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg’s uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks’ uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to...

On the Fourier transform of the symmetric decreasing rearrangements

Philippe Jaming (2011)

Annales de l’institut Fourier

Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the L 2 behavior of a Fourier transform of a function over a small set is controlled by the L 2 behavior of the Fourier transform of its symmetric decreasing rearrangement. In the L 1 case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...

On the non-equivalence of rearranged Walsh and trigonometric systems in L p

Aicke Hinrichs, Jörg Wenzel (2003)

Studia Mathematica

We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in L p for some p ≠ 2. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh-Paley order only.

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