Hardy-type inequalities for Hermite expansions.
Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted spaces
We investigate heat-diffusion and Poisson integrals associated with Laguerre and special Hermite expansions on weighted spaces with weights.
Henstock-Kurzweil type integrals in -adic harmonic analysis.
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.
Hilbert transforms associated with Dunkl-Hermite polynomials.
Imaginary powers of the Dunkl harmonic oscillator.
Inequalities for Walsh polynomials with semi-monotone and semi-convex coefficients.
Inequalities relative to two-parameter Vilenkin-Fourier coefficients
Integrability and -convergence of Rees-Stanojević sums with generalized semiconvex coefficients.
Integrability Theorems For Jacobi Series
Integrability theorems for trigonometric series
We show that, if the coefficients (an) in a series tend to 0 as n → ∞ and satisfy the regularity condition that , then the cosine series represents an integrable function on the interval [-π,π]. We also show that, if the coefficients (bn) in a series tend to 0 and satisfy the corresponding regularity condition, then the sine series represents an integrable function on [-π,π] if and only if . These conclusions were previously known to hold under stronger restrictions on the sizes of the differences...
Jacobi Polynomial Estimates and Fourier-Laplace Convergence.
Kantorovic Operators of Second Order.
Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
- and -discrepancy of (order 2) digital nets
Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...
Localization and summability of multiple Hermite series.
Maximal operators of two-dimensional Walsh-Fourier series.
Maximal operators of Fejér means of double Vilenkin-Fourier series
The main aim of this paper is to prove that the maximal operator of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space to the space weak-.
Maximal operators of Fejér means of Vilenkin-Fourier series.
Maximal operators of the Fejér means of the two dimensional character system of the -series field in the Kaczmarz rearrangement.