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 finite center, then L2,1 (G) * L2,1 (G) ⊆ L2,∞(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) = Supz∈B1/|B|∫B|f(z′)\dz′ is bounded from L2,1(X) to L2,∞(X) and from Lp(X) to Lp(X) in the sharp range of exponents p ∈ (2, ∞]. The supremum in the definition of M2f(z) is taken over all balls containing the point z.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty