The double difference property for some classes of functions (Q1396792)

The paper relates the difference property of \(F\) to the double-difference property of a pair \((F, F^{(2)})\), where \(F\) and \(F^{(2)}\) are classes of real-valued (and possibly periodical) functions of one and two real variables, respectively, sharing the same ``characterisation'' property. It is shown that under certain conditions, the double difference property of \((F, F^{(2)})\) is a consequence of the difference property of \(F\). Continuous, approximately continuous, pointwise discontinuous, \(N\)-essentially continuous and \(L_p\) (\(0<p\leq \infty \)) functions are all found to satisfy the double difference property.