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arXiv · 2203.13905

Variaiton and $λ$-jump inequalities on $H^p$ spaces

Sakin Demir
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Abstract

Let $ϕ\in \mathscr{S}$ with $\intϕ(x)\, dx=1$, and define $$ϕ_t(x)=\frac{1}{t^n}ϕ(\frac{x}{t}),$$ and denote the function family $\{ϕ_t\ast f(x)\}_{t>0}$ by $Φ\ast f(x)$. Suppose that there exists a constant $C_1$ such that $$\sum_{t>0} |\hatϕ_t(x)|^2 0$ such that $$\|\mathscr{V}_2(Φ\ast f)\|_{L^p}\leq C_2\|f\|_{H^p},\;\;\frac{n}{n+1} 0$ for some constant $C_3>0$.

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Sakin Demir. 2022-09-06. Variaiton and $λ$-jump inequalities on $H^p$ spaces. https://arxiv.org/abs/2203.13905

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