Some boundary fractal properties of the convolution transform of measures by an approximate identity
The authors relate the boundary behavior of a positive harmonic function to the local behavior of its boundary measure. As a consequence, if the measure is multifractal, so is the boundary behavior of the function. The harmonic function is the Poisson transform of the measure. The authors actually prove that similar relations hold between a measure and some of its integral transforms, called convolution transforms. It is related to the works of \textit{N. A. Watson} [J. Lond. Math. Soc., II. Ser. 21, 336-350 (1980; Zbl 0436.35038) and Ann. Acad. Sci. Fenn., Ser. A I, Math. 19, No.~1, 115-132 (1994; Zbl 0793.31001)].
scientific article; zbMATH DE number 1321986