STRONG ESTIMATE FOR SQAURE FUNCTIONS IN HIGHER DIMENSIONS
K. EL BERDAN
Abstract.
In this paper, we give a generalization to multidimensional case of strong estimate for square functions obtained by Jones Rosenblatt and Ostro-\break vskii Ref. 3. We assume that the averages are taken over squares and the operators are commuting and contraction in $L^2$. For the non-commutative case we need a supplementary condition. Some weak type inequalities are proved.
Compressed Postscript 
