Almost everywhere convergence of the inverse spherical transform on SL(2, R)

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.

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

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...

The surprising almost everywhere convergence of Fourier-Neumann series

For most orthogonal systems and their corresponding Fourier series, the study of the almost everywhere convergence for functions in L requires very complicated research, harder than in the case of the mean convergence. For instance, for trigonometric series, the almost everywhere convergence for functions in L is the celebrated Carleson theorem, proved in 1966 (and extended to L by Hunt in 1967...