부산대학교 도서관

Summary: ``The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local $L^p$ regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local $L^p$ regularity introduced by Jafard. We provide its characterization by a supremum of a wide range oriented anisotropic Triebel wavelet coefficients and leaders. In addition, we deduce estimates on the Hausdorf dimension of the set of points where the directional local $L^p$ regularity does not exceed a given value. The obtained results are illustrated by some examples of self-affine cascade functions.''