Almost Everywhere Convergence of Poisson Integrals on Tube Domains over Cones

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

Convergence of poisson integrals for bounded symmetric domains.

1. The purpose of this note is to describe the extension of the almost everywhere convergence of Poisson integrals to the case of the bounded symmetric domains of Cartan. It is useful to realize such a bounded symmetric domain D as a generalized upper half-plane (i.e., a Siegel domain of type II), and this is done as follows. Let V1 and V2 be two finite-dimensional vector spaces over C. Assume ...

Almost Everywhere Convergence of Series in L

We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence (ci) with ∑∞ i=1 |ci| = ∞, such that for every dynamical system (X,Σ, m, T ) and f ∈ L1(X), ∑∞i=1 cif(T ix) converges almost everywhere. A similar result is obtained in the real variable context.

On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms

We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi-Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the rst result on almost everywhere strong convergence in dimension greater than two.

On radial Fourier multipliers and almost everywhere convergence

We study a.e. convergence on L, and Lorentz spaces L, p > 2d d−1 , for variants of Riesz means at the critical index d( 1 2 − 1 p )− 1 2 . We derive more general results for (quasi-)radial Fourier multipliers and associated maximal functions, acting on L spaces with power weights, and their interpolation spaces. We also include a characterization of boundedness of such multiplier transformation...