Journal of the Australian Mathematical Society | |
Hardy-Littlewood maximal functions on some solvable Lie groups | |
G. Gaudry1  | |
[1] S. Giulini | |
关键词: primary 43 A 80; 22 E 30; secondary 42 B 25; | |
DOI : 10.1017/S1446788700032286 | |
学科分类:数学(综合) | |
来源: Cambridge University Press | |
【 摘 要 】
Let N be a nilpotent simply connected Lie group, and A a commutative connected d-dimensional Lie group of automorphisms of N which correspond to semisimple endomorphisms of the Lie algebra of N with positive eigenvalues. Form the split extension S = N × A ≅ N × a, a being the Lie algebra of A. We consider a family of “rectangles†Br in S, parameterized by r > 0, such that the measure of Br behaves asymptotically as a fixed power of r. One can construct the Hardy-Littlewood maximal function operator f → Mf relative to left translates of the family {Br}. We prove that M is of weak type (1, 1). This complements a result of J.-O. Strömberg concerning maximal functions defined relative to hyperbolic balls in a symmetric space.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040544003ZK.pdf | 151KB | download |