L^p(R^n)上的广义面积积分的推广

Extension of Generalized Area Integrals on L^p(R^n)

对于1<p<∞,给出了LpR(n)上的广义面积积分更广泛的定义,即Aμ(f)(η)=∫r|η||(Φt*(f)(x)|dμ(x,t)/tn;在这种定义下,广义面积积分是有界的充要条件是μ为Carleson测度之间的关系.

In this paper for 1〈p〈∞,the definition of extention of generalized area integrals on L^p（R^n） is given, i. e.Aμ（f）（η）=∫Г〈η〉｜（φ1＊f）（x）｜dμ（x,t）/t^nAnd the necessary and sufficient condition ofgiven generalized area integrals＂ boundness the authors obtain is that μ is a Carleson measure.