Weighted $L^p$ estimates of Kato square roots associated to degenerate elliptic operators
Year: 2017
Type: article
Abstract: Let $w$ be a Muckenhoupt $A_2({\\mathbb R}^n)$ weight and\n$L_w:=-w^{-1}\\operatorname{div}(A\\nabla)$ the degenerate elliptic operator on the\nEuclidean space ${\\mathbb R}^n$, $n\\geq 2$. In this article, the authors establish some\nweighted $L^p$ estimates of Kato square roots associated to the degenerate elliptic\noperators $L_w$. More precisely, the authors prove that, for $w\\in A_{p}({\\mathbb R}^n)$,\n$p\\in(\\frac{2n}{n+1},2]$ and any $f\\in C^\\infty_c({\\mathbb R}^n)$,\n$\\|L_w^{1/2}(f)\\|_{L^p(w,{\\mathbb R}^n)} \\sim \\|\\nabla f\\|_{L^p(w,{\\mathbb R}^n)}$, where\n$C_c^\\infty({\\mathbb R}^n)$ denotes the set of all infinitely differential functions with\ncompact supports and the implicit equivalent positive constants are independent of\n$f$.
Source: Publicacions Matemàtiques
Authors: D. Yang, J. Zhang
Institution: Beijing Normal University
Language: Catalan
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2963301816