A Note on the Boundedness of Doob Maximal Operators on a Filtered Measure Space

Wei Chen and Jingya Cui
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Wei Chen: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
Jingya Cui: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Mathematics, 2021, vol. 9, issue 22, 1-12

Abstract: Let M be the Doob maximal operator on a filtered measure space and let v be an A p weight with 1 < p < + ? . We try proving that ? M f ? L p ( v ) ? p ? [ v ] A p 1 p ? 1 ? f ? L p ( v ) , where 1 / p + 1 / p ? = 1 . Although we do not find an approach which gives the constant p ? , we obtain that ? M f ? L p ( v ) ? p 1 p ? 1 p ? [ v ] A p 1 p ? 1 ? f ? L p ( v ) , with lim p ? + ? p 1 p ? 1 = 1 .

Keywords: filtered measure space; Doob maximal operator; weighted inequality; principal set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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