Estimates for Parameter Littlewood-Paley gκ⁎ Functions on Nonhomogeneous Metric Measure Spaces. (11th April 2016)

• Record Type: Journal Article
• Authors: Lu, Guanghui; Tao, Shuangping
• Other Names: Sawano Yoshihiro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-04-11
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/9091478
• Languages: English
• ISSNs: 2314-8896

Abstract

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 ) .