Criteria of pointwise and uniform directional Lipschitz regularities on tensor products of Schauder functions (Q681763)

The authors derive a criterion for uniform directional Lipschitz regularity of a multi-parameter function \(f\) using decay conditions on the on the coefficients of \(f\) in a tensor product Schauder basis. As a consequence, they obtain a characterization of the local critical directional Lipschitz regularity of \(f\). The results are then applied to multi-dimensional parameter fractional Wiener fields in \(\mathbb R^d\) and Sierpiński cascade functions. Finally, criteria for the point-wise directional Lipschitz regularity of \(f\) employing decay conditions on either two progressive differences in the given direction or the coefficients of the function in a tensor product Schauder basis are exhibited.