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

Author

Listed:
  • Wei Chen

    (School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China)

  • Jingya Cui

    (School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China)

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 .

Suggested Citation

  • Wei Chen & Jingya Cui, 2021. "A Note on the Boundedness of Doob Maximal Operators on a Filtered Measure Space," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2953-:d:682648
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