Examples of metric measure spaces related to modified Hardy-Littlewood maximal operators

Boundedness for Multilinear Littlewood-Paley Operators on Hardy and Herz-Hardy Spaces

Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...

Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...

On the Variation of the Hardy–littlewood Maximal Function

We show that a function f : R → R of bounded variation satisfies VarMf ≤ C Var f, where Mf is the centered Hardy–Littlewood maximal function of f . Consequently, the operator f 7→ (Mf) is bounded from W (R) to L(R). This answers a question of Hajłasz and Onninen in the one-dimensional case.

Mathematische Zeitschrift Some remarks on the Hardy-Littlewood maximal function on variable L spaces

We show that any pointwise multiplier for BMO(R) generates a function p from the class P(Rn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable L space. In particular, this gives a positive answer to Diening’s conjecture saying that there are discontinuous functions which nevertheless belong to P(Rn). Mathematics Subject Classification (2000): 42B25

Orlicz Spaces for Which the Hardy-littlewood Maximal Operator Is Bounded