Endpoint Estimates for Generalized Commutators of Hardy Operators on H1 Space

Abstract EN

We study the H1-boundedness of the generalized commutators of Hardy operator with a homogeneous kernel as follows: ℋΩ,A,βmf(x)=(1/|x|n-β)∫|y|<|x|(Ω(x-y)/|x-y|m-1)Rm(A;x,y)f(y)dy, where Rm(A;x,y)=A(x)-∑|α|

We prove that, when m≥1, ℋΩ,A,βm is not bounded from H1 to Ln/(n-β) unless ℋΩ,A,βm≡0.

Finally, we prove that ℋΩ,A,βm is bounded from H1 to Ln/(n-β),∞ with m≥1.