On a singular integral
On a singular integral
On a sum of Vinogradov
On a Szegö's theorem of orthogonal polynomials.
It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.
On a Theorem of Ingham.
On a theorem of Kłosowska about generalised convolutions
On a theorem of Saeki concerning convolution squares of singular measures
If , then there exists a probability measure such that the Hausdorff dimension of the support of is and is a Lipschitz function of class .
On a version of Littlewood-Paley function
On a weak type (1,1) inequality for a maximal conjugate function
In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.
On -summability of orthogonal series
In the paper, we prove two theorems on summability, , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
On Abel summability of multiple Jacobi series
On a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
On almost everywhere and mean convergence of Hermite and Laguerre expansions
On Almost Everywhere Convergence.
On almost summability of conjugate Fourier series.
On almost periodicity defined via non-absolutely convergent integrals
We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.
On an approximation of function and its derivatives.
On an extension of a theorem of O. Szàsz
On an extension of singular integrals along manifolds of finite type.
On an extrapolation theorem of Carleson-Sjölin type with applications to a.e. convergence of Fourier series