摘要
In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).
In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).
