A characterization of localized Bessel potential spaces and applications to Jacobi and Henkel multipliers
A correction to the paper "A multiplier theorem for Jacobi expansion" Studia Math. 52 (1975), pp. 234-261
A Fast Transform for Spherical Harmonics.
A multiplier theorem for Jacobi expansions
A new approach to the problem of constructing recurrence relations for the Jacobi coefficients
A note on weights: Pasting weights and changing variables.
A note on certain partial sum operators
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
A note on the magnitude of Walsh Fourier coefficients.
A note on the means
A Paley type inequality for two-parameter Vilenkin-Fourier coefficients.
A proof of Pełczyński's conjecture for the Haar system
A remark on the multipliers of the Haar basis of L¹[0,1]
A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
A survey of weighted polynomial approximation with exponential weights.
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A uniform estimate for quartile operators.
There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...
Absolute convergence of the double series of Fourier-Haar coefficients.
Almost everywhere convergence of Laguerre series
Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers
We prove the almost everywhere convergence of the Marcinkiewicz means of integrable functions σₙf → f for every f ∈ L¹(I²), where I is the group of 2-adic integers.
Almost everywhere convergence of some summabillity methods for Laguerre series
Almost everywhere convergence of subsequence of logarithmic means of Walsh-Fourier series.