Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0<p≤1 and 1<u≤∞,such ...Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0<p≤1 and 1<u≤∞,such that the commutator[b,T]is bounded from weighted Hardy space H_(ω)^(p)(R^(n))to weighted Lebesgue space L_(ω)^(p)(R^(n))if b∈BMO_(ω,p,∞)(R^(n)),and is bounded from weighted Hardy space H_(ω)^(p)(R^(n)) to itself if T^(∗)1=0 and b∈BMO_(ω,p,u)(R^(n))for 1<u<2.展开更多
In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥0.Under these new smoothness conditions,we will prove the boundedness properties of singu...In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥0.Under these new smoothness conditions,we will prove the boundedness properties of singular integral operators TΩ,fractional integrals TΩ,α and parametric Marcinkiewicz integrals μΩρ with variable kernels on the Hardy spaces Hp（Rn） and weak Hardy spaces WHP（Rn）.Moreover,by using the interpolation arguments,we can get some corresponding results for the above integral operators with variable kernels on Hardy-Lorentz spaces Hp,q（Rn） for all p 〈 q 〈 ∞.展开更多
基金Supported by the NNSF of China(Grant Nos.11771358,11871101,12171399)。
文摘Let T be a strongly singular Calderon-Zygmund operator and b∈L_(loc)(R^(n)).This article finds out a class of non-trivial subspaces BMO_(ω,p,u)(R^(n))of BMO(R^(n))for certain ω∈A_(1),0<p≤1 and 1<u≤∞,such that the commutator[b,T]is bounded from weighted Hardy space H_(ω)^(p)(R^(n))to weighted Lebesgue space L_(ω)^(p)(R^(n))if b∈BMO_(ω,p,∞)(R^(n)),and is bounded from weighted Hardy space H_(ω)^(p)(R^(n)) to itself if T^(∗)1=0 and b∈BMO_(ω,p,u)(R^(n))for 1<u<2.
文摘In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥0.Under these new smoothness conditions,we will prove the boundedness properties of singular integral operators TΩ,fractional integrals TΩ,α and parametric Marcinkiewicz integrals μΩρ with variable kernels on the Hardy spaces Hp（Rn） and weak Hardy spaces WHP（Rn）.Moreover,by using the interpolation arguments,we can get some corresponding results for the above integral operators with variable kernels on Hardy-Lorentz spaces Hp,q（Rn） for all p 〈 q 〈 ∞.
