ON ABSOLUTE VALUES OF QK FUNCTIONS

In this paper, the effect of absolute values on the behavior of functions f in the spaces Q(K) is investigated. It is clear that g is an element of Q(K)(partial derivative D) double right arrow vertical bar g vertical bar is an element of Q(K)(partial derivative D), but the converse is not always true. For f in the Hardy space H-2, we give a condition involving the modulus of the function only, such that the condition together with vertical bar f vertical bar is an element of Q(K)(partial derivative D) is equivalent to f is an element of Q(K). As an application, a new criterion for inner-outer factorisation of Q(K) spaces is given. These results are also new for Q(p) spaces.