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The Triangle Averaging Operator
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.jfa.2020.108671
Eyvindur A. Palsson , Sean R. Sovine

Abstract We examine the averaging operator T corresponding to the manifold in R 2 d of pairs of points ( u , v ) satisfying | u | = | v | = | u − v | = 1 , so that { 0 , u , v } is the set of vertices of an equilateral triangle. We establish L p × L q → L r boundedness for T for ( 1 / p , 1 / q , 1 / r ) in the convex hull of the set of points { ( 0 , 0 , 0 ) , ( 1 , 0 , 1 ) , ( 0 , 1 , 1 ) , ( 1 / p d , 1 / p d , 2 / p d ) } , where p d = 5 d 3 d − 2 .

中文翻译:

三角平均算子

摘要 我们研究了对应于 R 2 d 中满足 | 的点对 ( u , v ) 中的流形的平均算子 T。你| = | v | = | u - v | = 1 ,所以 { 0 , u , v } 是等边三角形的顶点集。我们在点集 { ( 0 , 0 , 0 ) , ( 1 , 0 , ) 的凸包中为 T 建立 L p × L q → L r 有界性 ( 1 / p , 1 / q , 1 / r ) 1 ) , ( 0 , 1 , 1 ) , ( 1 / pd , 1 / pd , 2 / pd ) } , 其中 pd = 5 d 3 d − 2 。
更新日期:2020-11-01
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