On the almost everywhere convergence to $L\sp p$ data for higher order hyperbolic operators

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.

Order Almost Dunford-Pettis Operators on Banach Lattices

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

On Almost Everywhere Convergence of Bochner-riesz Means in Higher Dimensions

In Rn define (TXirf)~(£) = /(£)(! k_1í2l)+If n > 3, A > ¿(n-l)/(n+l)and2 and the associated maximal operators are r;/(x) = suP|(/-(i-Ki2)i)-|(x). r>0 It is conjectured that, when A > 0, T\ is bounded on Lp if and only if pó(A) < p < Po(A), where po(A)...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes

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...