Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces. (11th April 2016) - Lu, Guanghui; Tao, Shuangping
Abstract : Let ( X, d, μ ) be a metric measure space which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of M κ ⁎ satisfies a certain Hörmander-type condition, M κ ⁎, ρ is bounded from Lebesgue spaces L p ( μ ) to Lebesgue spaces L p ( μ ) for p ≥ 2 and is bounded from L 1 ( μ ) into L 1, ∞ ( μ ) . As a corollary, M κ ⁎, ρ is bounded on L p ( μ ) for 1 < p < 2 . In addition, the authors also obtain that M κ ⁎, ρ is bounded from the atomic Hardy space H 1 ( μ ) into the Lebesgue space L 1 ( μ ) .