Weak and strong types estimates for square functions associated with operators
| Autor: | Cao, Mingming, Si, Zengyan, Zhang, Juan |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical square function $S_{\alpha,L}$ associated with an abstract operator $L$. We first establish two-weight inequalities including bump estimates, and Fefferman-Stein inequalities with arbitrary weights. We also present the local decay estimates using the extrapolation techniques, and the mixed weak type estimates corresponding Sawyer's conjecture by means of a Coifman-Fefferman inequality. Beyond that, we consider other weak type estimates including the restricted weak-type $(p, p)$ for $S_{\alpha, L}$ and the endpoint estimate for commutators of $S_{\alpha, L}$. Finally, all the conclusions aforementioned can be applied to a number of square functions associated to $L$. Comment: 28 pages. arXiv admin note: text overlap with arXiv:2009.13814 |
| Databáze: | arXiv |
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