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Pré-Publication, Document De Travail Année : 2021

Optimal orders of the best constants in the Littlewood-Paley inequalities

Résumé

Let $\{\mathbb{P}_t\}_{t>0}$ be the classical Poisson semigroup on $\mathbb{R}^d$ and $G^{\mathbb{P}}$ the associated Littlewood-Paley $g$-function operator: $$G^{\mathbb{P}}(f)=\Big(\int_0^\infty t|\frac{\partial}{\partial t} \mathbb{P}_t(f)|^2dt\Big)^{\frac12}.$$ The classical Littlewood-Paley $g$-function inequality asserts that for any $1

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hal-03242491 , version 1 (31-05-2021)

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Quanhua Xu. Optimal orders of the best constants in the Littlewood-Paley inequalities. 2021. ⟨hal-03242491⟩
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