2024/08/05 by Peng Chen, Minxing Shen, Chen, Peng +5
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2408.02180
In this article we investigate Lp boundedness of the spherical maximal operator \mathfrakmα of (complex) order α on the n-dimensional hyperbolic space ℍn, which was introduced and studied by El Kohen. We prove that when n≥ 2, for α∈ℝ and 11-n+n/p for 1 max \(2-n)/p-1/(p pn),(2-n)/p- (p-2)/[p pn(pn-2)]\ for 2≤ p≤ ∞, with pn=2(n+1)/(n-1) for n≥ 3 and pn=4 for n=2.