非齐度量测度空间上Marcinkiewicz交换子的Lipschitz估计

Lipschitz estimates for Marcinkiewicz commutator on non-homogeneous metric measure spaces

设(x,d,μ)是一个满足上双倍条件和几何双倍条件的度量测度空间.证明了Marcinkiewicz积分M与Lip_β(μ)函数b生成的交换子M_b的(L^p(μ),L^q(μ))型和(L^1(μ),L^n/(n-β)·∞(μ))型不等式.得到交换子M_b是从Hardy空间H^1(μ)到L^n/(n-β)(μ)上有界的.

Let（x,d,μ） be a measure space satisfying the upper doubling condition and the geometrically doubling condition,the inequalities of type（Lp（μ）,Lq（μ）） and type（L1（μ）,Lπ/（n-β）·∞（μ）） are obtained for the Marcinkiewicz commutator M_b generated by the Marcinkiewicz integral operator M and the Lipβ（μ） function b.It was shown that the commutator M_b is bounded from Hardy spaces H1（μ） into the spaces Ln/（n-β）（μ）.