A strong version of Poisson summation.
A study of the real Hardy inequality.
A study on degree of approximation by summability means of the Fourier-Laguerre expansion.
A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform
Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform and also all weighted dyadic martingale transforms are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.
A survey of certain results on strong approximation by orthogonal series
This is a survey of results in a particular direction of the theory of strong approximation by orthogonal series, related mostly with author's contributions to the subject.
A Tauberian theorem for distributions
The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.
A theorem for Fourier coefficients of a function of class .
A theorem of Cesari on mulitple Fourier series
A theorem on the absolute Riesz summability factors of a Fourier series
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...
A Universal Topology for Sequence Spaces.
A variation norm Carleson theorem
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
A Weighted Tauberian Theorem.
About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system.
Absolute convergence of Fourier series of a function of Wiener’s class
Absolute convergence of Fourier series on finite-dimensional groups
Absolute convergence of multiple Fourier integrals
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.
Absolute Nörlund summability factors of power series and Fourier series
Four theorems of Ahmad [1] on absolute Nörlund summability factors of power series and Fourier series are proved under weaker conditions.
Absolute Nörlund summability factors of power series and Fourier series
Absolute Riesz summability of Fourier series