INTRINSIC SQUARE FUNCTION CHARACTERIZATIONS OF WEAK MUSIELAK-ORLICZ HARDY SPACES

Let phi : R-n x [0, infinity) -> [0, infinity) satisfy that, for any given x is an element of R-n, phi(x, .) is an Orlicz function and phi(., t) is a Muckenhoupt A(infinity)(R-n) weight uniformly in t is an element of (0, infinity). In this article, via using the atomic and Littlewood-Paley function characterizations of the weak Musielak-Orlicz Hardy space WH phi(R-n), for any alpha is an element of (0, 1] and s is an element of Z(+), we first establish its s-order intrinsic square function characterizations in terms of the intrinsic Lusin area function S-alpha,S-s, the intrinsic g-function g alpha,s and the intrinsic g(lambda)*-function g(lambda,alpha,s)* with the best known range lambda is an element of(2+2(alpha+s)/n,infinity).