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.
Bessel generalized translations and some problems of approximation theory for functions on the half-line.
BMO and commutators of martingale transforms
The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on , , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.
Continuous rearrangements of the Haar system in for 0 < p < ∞
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
Critical length for a Beurling type theorem
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.
Decreasing Rearranged Fourier Series.
Dunkl-Gabor transform and time-frequency concentration
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...
Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization.
Gegenbauer polynomials and semiseparable matrices.
Generalized conjugate systems on local fields
Gibbs' Phenomenon and Arclength.
Hardy's inequality for compact Lie groups.
Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
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.
Imaginary powers of the Dunkl harmonic oscillator.
Mapping properties of fundamental operators in harmonic analysis related to Bessel operators
We obtain sharp power-weighted , 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.
Multipliers of the Fourier-Haar series.
Note on decreasing rearrangement of Fourier series.
On the absolute summability of series with respect to block-orthonormal systems.
On the Fourier transform of the symmetric decreasing rearrangements
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 behavior of a Fourier transform of a function over a small set is controlled by the behavior of the Fourier transform of its symmetric decreasing rearrangement. In the 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
We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in 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.