### A dispersion inequality in the Hankel setting

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.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

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.

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

We prove three theorems on linear operators ${T}_{\tau ,p}:{H}_{p}\left(\mathcal{B}\right)\to {H}_{p}$ induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for ${T}_{\tau ,p}$ to be continuous for 0 < p < ∞.

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.

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...

The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.

We obtain sharp power-weighted ${L}^{p}$, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.

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...

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.