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Wu-yi Pan

Publications and source records attributed to Wu-yi Pan.

5 recordsLinked to original sources
arXiv2022

A remark on the Hardy-Littlewood maximal functions

We investigate the magnitude relation of the non-centered Hardy-Littlewood maximal operators and centered one. By using a discretization technique, we prove two facts: the first one is that the space is ultrametric if and only if the two maximal operators are identical for all discrete measure; the second is, the uncentred maximal operator is strictly greater than the centered one if $(M,d_g)$ is a Riemannian manifold and $μ$ is the Riemannian volume measure.

math.CA↗
arXiv2022

Fixed points of the uncentered Hardy-Littlewood maximal operator

We give a survey, known and new results on the beingness of fixed points of the maximal operator in the more general settings of metric measure space. In particular, we prove that the fixed points of the uncentered one must be the constant function if the measure satisfies a mild continuity assumption and its support is connected.

math.MG↗
arXiv2022

Limiting weak type behaviors of maximal operator on the positive real axis

In this note, we establish a discrete method to characterize the limiting weak type behaviors of the centered Hardy-Littlewood maximal operator on the positive real axis through testing on Dirac deltas. As an application, we give some new examples of the limiting weak-type behaviors of the maximal operator associated with several special measures.

math.MG↗
arXiv2022

Lower bounds for uncentered maximal functions on metric measure space

We show that the uncentered Hardy-Littlewood maximal operators associated with the Radon measure $μ$ on $\mathbb{R}^d$ have the uniform lower $L^p$-bounds (independent of $μ$) that are strictly greater than $1$, if $μ$ satisfies a mild continuity assumption and $μ(\mathbb{R}^d)=\infty$. We actually do that in the more general context of metric measure space $(X,d,μ)$ satisfying the Besicovitch covering property. In addition, we also illustrate that the continuity condition can not be ignored by constructing counterexamples.

math.MG↗