The Hardy--Littlewood maximal operator and BLO1/log class of exponents

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...

Regularity of the Hardy-littlewood Maximal Operator on Block Decreasing Functions

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l∞-norm, that is, by a...

An Elementary Approach to Several Results on the Hardy-littlewood Maximal Operator

We give new elementary proofs of theorems due to B. Muckenhoupt, B. Jawerth, and S. Buckley. By means of our approach we answer a question raised by J. Orobitg and C. Pérez.

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.

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