Bilinear singular integral operators with kernels in weighted spaces

Autor:	Honzík, Petr, Lappas, Stefanos, Slavíková, Lenka
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	We study boundedness properties of one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $\Omega$ to the unit sphere $\mathbb S^1$ has vanishing integral and belongs to $L^q(\mathbb S^1)$ for some $q>1$. Under the additional assumption that $\Omega$ is supported away from certain degenerate points, we establish the full quasi-Banach range of $L^{p_1}(\mathbb R) \times L^{p_2}(\mathbb R) \rightarrow L^p(\mathbb R)$ bounds, corresponding to any $10$ and for any $(\theta_1,\theta_2)\in \mathbb S^1$. In addition, we provide counterexamples that show the failure of the $n$-dimensional version of our result when $n\geq 2$, as well as the failure of its $m$-linear variant in dimension one when $m\geq 3$. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.07014 Zobrazit plný text záznamu View this record from Arxiv