# For Haagerup spaces \$ L ^ {P} \$

There is a definition in Haagerup's article on $$L ^ {P}$$ spaces for the weights, my question is after putting the norm is it become semi-finished $$L ^ {P}$$ space on the cross product? I am not clear please help. How the norm on L ^ {P} space is related to weight $$varphi$$?