Lower bounds for the weak type (1, 1) estimate for the maximal function associated to cubes in high dimensions
نویسندگان
چکیده
منابع مشابه
The Weak Type (1, 1) Bounds for the Maximal Function Associated to Cubes Grow to Infinity with the Dimension
Let Md be the centered Hardy-Littlewood maximal function associated to cubes in R with Lebesgue measure, and let cd denote the lowest constant appearing in the weak type (1,1) inequality satisfied by Md. We show that cd → ∞ as d → ∞, thus answering, for the case of cubes, a long standing open question of E. M. Stein and J. O. Strömberg.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2013
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2013.v20.n5.a7