An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators

By A. Ionescu. 2000

52 citations recorded by the source corpus.

One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with flnite center, then L 2;1 (G)⁄L 2;1 (G)µ L 2;1 (G): Let K be a maximal compact subgroup of G and X = G=K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M2f(z) = sup2B 1 jBj Z B jf(z 0 )jdz 0 is bounded from L 2;1 (X )t oL 2;1 (X) and from L p (X )t oL p (X) in the sharp range of exponents p2 (2;1]. The supremum in the deflnition ofM2f(z )i s taken over all balls containing the point z.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4ee148fa8d82c00a145229ebd29eecf3dfef495f

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The wave equation on hyperbolic spaces (2010, methodology): “In Section 5 we first deduce dispersive L ′ →Lq estimates for W (σ,τ) t , when 2<q<∞, by using interpolation and the Kunze–Stein phenomenon [5, 6, 23].”
Semilinear Schrödinger flows on hyperbolic spaces: scattering in H1 (2008, background): “3 This gain is related to the Kunze–Stein phenomenon L 2 (G) ∗ L p (G) ⊆ L 2 (G) for any p ∈[ 1, 2) ,w here G is the Lorentz group SO (d, 1) ,s ee [22, 28 ,35].”