New bounds on Cantor maximal operators
نویسندگان
چکیده
We prove $L^p$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our improve upon those obtained by I. Łaba and M. Pramanik in some cases are sharp up endpoint. A consequence our main result is that there exist Salem Cantor sets any dimension $>1/2$ such operator bounded on $L^2(\mathbb{R})$. follow overall scheme Łaba-Pramanik analytic part argument, while probabilistic instead inspired earlier work intersection properties random measures.
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ژورنال
عنوان ژورنال: Revista De La Union Matematica Argentina
سال: 2022
ISSN: ['0041-6932', '1669-9637']
DOI: https://doi.org/10.33044/revuma.3170