Weighted reverse weak type inequalities for the ergodic maximal function and the classes $L{\rm log}\sp +L$

Weighted Weak-type Inequalities for the Maximal Function of Nonnegative Integral Transforms over Approach Regions

The relation between approach regions and singularities of nonnegative kernels Kt(x, y) is studied, where t ∈ (0,∞), x, y ∈ X, and X is a homogeneous space. For 1 ≤ p < q < ∞, a sufficient condition on approach regions Ωa (a ∈ X) is given so that the maximal function sup (x,t)∈Ωa ∫ X Kt(x, y)f(y) dσ(y) is weak-type (p, q) with respect to a pair of measures σ and ω. It is shown that this conditi...

Weak type inequalities for maximal operators associated to double ergodic sums

Given an approach region Γ ∈ Z+ and a pair U , V of commuting nonperiodic measure preserving transformations on a probability space (Ω,Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L(Ω) converge a.e. or that, given a positive increasing function φ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lφ(L) (Ω) whose associated multipa...

Weighted Norm Inequalities for the Local Sharp Maximal Function

Sharp Weighted Inequalities for the Vector–valued Maximal Function

We prove in this paper some sharp weighted inequalities for the vector–valued maximal function Mq of Fefferman and Stein defined by Mqf(x) = ( ∞ ∑ i=1 (Mfi(x)) q )1/q , where M is the Hardy–Littlewood maximal function. As a consequence we derive the main result establishing that in the range 1 < q < p < ∞ there exists a constant C such that ∫ Rn Mqf(x) p w(x)dx ≤ C ∫ Rn |f(x)|qM [ p q ]+1 w(x)d...

the investigation of the relationship between type a and type b personalities and quality of translation

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