A note on inhomogeneous Triebel-Lizorkin space associated with sections

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Title:	A note on inhomogeneous Triebel-Lizorkin space associated with sections
Authors:	林靖容;Lin, Jing-Rong
Contributors:	數學系
Keywords:	Triebel-Lizorkin space;sections
Date:	2019-01-14
Issue Date:	2019-04-02 15:09:53 (UTC+8)
Publisher:	國立中央大學
Abstract:	在這篇文章中，我們討論R^n上特定的section，就是固定x為中心、以√t為半徑的球體B(x,√t)，其勒貝格測度等價於t^(n/2)，因此可以考慮關於此section的非齊性F_pq^s (R^n )，當任意兩點x,y滿足\|x-y\|≥1時，Monge-Ampère奇異積分算子H有\|D_0 HD_0 (x,y)\|≤\|x-y\|^(-2)的條件，即可證明H在F_pq^s (R^n )上有界。;In this paper, we consider the special section on R^n, which is a ball centered at with radius √t, and the Lesbegue measure of this section is equivalent to t^(n/2). Then, define the inhomogenous Triebel-Lizorkin space F_pq^s (R^n ) associated with such sections, and show that the Monge-Ampère singular integral operator H is bounded on F_pq^s (R^n ) if \|D_0 HD_0 (x,y)\|≤\|x-y\|^(-2) for any x,y∈R^n,\|x-y\|≥1.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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