Boundedness of Marcinkiewicz integrals on Hardy spaces HSUPp/SUP over non-homogeneous metric measure spaces

摘要

Under the assumption that (X , d, μ ) is a non-homogeneous metric measure space, the authors prove that the Marcinkiewicz integral operator is bounded from the molecular Hardy space H p,q, γ , ε mb, ρ ( μ ) (or the atomic Hardy space H p, q, γ atb, ρ ( μ )) into the Lebesgue space L p ( μ ). To this end, some boundedness criteria on these Hardy spaces are established.