Lp-summability of Riesz means for the sublaplacian on complex spheres

Summability of Multi-Dimensional Trigonometric Fourier Series

We consider the summability of oneand multi-dimensional trigonometric Fourier series. The Fejér and Riesz summability methods are investigated in detail. Different types of summation and convergence are considered. We will prove that the maximal operator of the summability means is bounded from the Hardy space Hp to Lp, for all p > p0, where p0 depends on the summability method and the dimensio...

About summability of Fourier-Laplace series

Abstract In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater than critical index N−1 2 we established the estimation for maximal operator of the Riesz means. Note that when order α of Riesz means is less than cr...

About the Almost Everywhere Convergence of the Spectral Expansions of Functions

Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...

Spectra of Bochner-Riesz means on L

The Bochner-Riesz means are shown to have either the unit interval [0, 1] or the whole complex plane as their spectra on Lp, 1 ≤ p <∞

Summability of the l-1 Cesàro means of an integral transformation connected to a Riesz potential