INTRINSIC SQUARE FUNCTION CHARACTERIZATIONS OF MUSIELAK-ORLICZ HARDY SPACES

Let phi : R-n x [0, infinity). [0, infinity) be such that phi(x, .) is an Orlicz function and infinity(., t) is a Muckenhoupt A(infinity)(R-n) weight uniformly in t. In this article, for any alpha is an element of (0, 1] and s is an element of Z(+), the authors establish the s-order intrinsic square function characterizations of H-phi(R-n) 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,a,s)* with the best known range lambda is an element of (2 + 2(alpha + s)/n, infinity), which are defined via Lip(alpha)(R-n) functions supporting in the unit ball. A phi-Carleson measure characterization of the Musielak-Orlicz Campanato space L-phi,(1,s)(R-n) is also established via the intrinsic function. To obtain these characterizations, the authors first show that these s-order intrinsic square functions are pointwise comparable with those similar-looking s-order intrinsic square functions defined via Lip(alpha) (R-n) functions without compact supports, which when s = 0 was obtained by M. Wilson. All these characterizations of H-phi(R-n), even when s = 0 phi(x, t) := w(x)(tp) for all t is an element of [0, infinity) and x is an element of R-n with p is an element of (n/(n + alpha), 1] and w is an element of A(p(1+alpha/n))(R-n), also essentially improve the known results.