Weak and strong type estimates for the multilinear Littlewood-Paley operators
| Autor: | Cao, Mingming, Hormozi, Mahdi, Ibañez-Firnkorn, Gonzalo, Rivera-Ríos, Israel P., Si, Zengyan, Yabuta, Kôzô |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in terms of aperture $\alpha$ and $\vec{w} \in A_{\vec{p}}$. By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise $A_{\infty}$ norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley $g^*_{\lambda}$ function. Some results are new even in the linear case. Comment: 35pages, Some new results have been added |
| Databáze: | arXiv |
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