On the weak-type (1,1) of the uncentered Hardy–Littlewood maximal operator associated with certain measures on the plane
On the weak-type (1,1) of the uncentered Hardy–Littlewood maximal operator associated with certain measures on the plane
Suppose μ is a positive measure on $\mathbb{R}^{2}$ given by μ=ν×λ, where ν and λ are Radon measures on $\mathcal{S}^{1}$ and $\mathbb{R}^{{\mathchoice {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .1ex\hbox {$\scriptscriptstyle +$}} {\scriptscriptstyle +}}}$, respectively, which do not vanish on any open interval. We prove that if for …