In this paper, we give a new proof of a result of R. Jones showing almost everywhere convergence of spherical means of actions of R on L(X)-spaces are convergent for d ≥ 3 and p > d d− 1 . This is done by adapting the proof of the spherical maximal theorem by Rubio de Francia so as to obtain directly the ergodic theorem.

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like ∃≥3/4y, which says that “for at least 3/4 of all y”. These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifi...

Abstract In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces L p (ℝ n ), Hardy H ) general mixed norm spaces, which implies almost everywhere convergence of such operator. this paper, we study rate some sobolev type spaces.

We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The is defined two matrices and we show that it measurably isomorphic to shift on set $\{1,2\}^\mathbb{N}$ of directive sequences. For given $\mathcal{C}$ substitutions, there exists $\mathcal{C}$-adic sequence for every vector letter frequencies or, equivalently, sequence....