非齐型空间上奇异积分算子加权估计

Weighted Estimates for Singular Integral Operators on Non-homogeneous Spaces

让μ是Rd上非双倍的Radon测度,μ仅满足增长性条件,即存在c0>0,对所有x∈Rd,r>0,μ(B(x,r))≤c0rn成立,其中0<n≤d。学习在非双倍测度的条件下,具有Dini核的极大奇异积分算子是从L1( ω)到L1,∞( ω)和Lp( ω)有界的,其中1<p<∞,( ω)∈Ap。

Let μ be a Radon measure on R^d which may be non doubling, the only condition that μ must satisfy is growth condition,namely there is a constant c_0>0,such that μ(B(x,r))≤c_0r^n,for all x∈R^d,r>0,and for some fixed 0<n≤d.To study that maximal singular integral operators with Dini kernels are from L^1 to L^(1,∞) and L^p bounded for 1<p<∞ if ∈A_p.