在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分...在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分量的参数表达.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
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 〈 ∞.
