Estimates for Parameter Littlewood-Paley g κ ⁎ Functions on Nonhomogeneous Metric Measure Spaces

Abstract EN

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 ) .