Weak type inequalities for the maximal ergodic function and the maximal ergodic Hilbert transform in weighted spaces
Ergodic power functions for mean bounded, invertible, positive operators
Weights for ergodic square functions
On the Pointwise Ergodic Theorem in
Weighted weak type inequalities for the ergodic maximal function and the pointwise ergodic theorem
Some weighted inequalities for general one-sided maximal operators
We characterize the pairs of weights on ℝ for which the operators are of weak type (p,q), or of restricted weak type (p,q), 1 ≤ p < q < ∞, between the Lebesgue spaces with the coresponding weights. The functions h and k are positive, h is defined on , while k is defined on . If , , 0 ≤ β ≤ α ≤ 1, we obtain the operator . For this operator, under the assumption 1/p - 1/q = α - β, we extend the weak type characterization to the case p = q and prove that in the case of equal weights and...
Ergodic transforms associated to general averages
Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in , 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in . For p = 1 we find that the maximal ergodic...
Differential transforms of Cesàro averages in weighted spaces .
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