BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL RELATED TO MULTILINEAR COMMUTATORS WITH VARIABLE KERNELS ON HARDY SPACES

摘要

Let b = (b1,b2,··· ,bm),bi ∈Λ˙βi(Rn),1 ≤ i ≤ m,βi > 0, sum from i=1 to m()βi = β,0 < β < 1, μΩ,b(f)(x) =(integral from n=0 to ∞|Fb,t(f)(x)|2dt/3t) 2/1 , Fb,t(f)(x) =∫ |x-y|≤tΩ|(x,x-y)/|x-y|n-1) multiply from i=1 to m() [bi(x)-bi(y)]f(y)dy. We consider the boundedness of μ?,b on Hardy type space Hbp (Rn).