Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite meas...Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.展开更多
文摘Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.
