Date | 2024-03-29 |
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Speaker | Zhendong Xu |

Dept. | 서울대학교 |

Room | 129-309 |

Time | 10:00-12:00 |

We prove the pointwise equivalence between the Littelewood-Paley-Stein g-function of a semigroup and the martingale square function. This equivalence can also extend to the vector-valued and noncommutative settings. Our argument relies on the construction of a special symmetric diffusion semigroup associated with a martingale filtration. As an application, we obtain some optimal orders of the constants in the Littlewood-Paley-Stein inequality. We are also seeking for further applications to the vector-valued and noncommutative harmonic analysis.

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