Pointwise convergence to the initial data for nonlocal dyadic diffusions

ACTIS MARCELO; AIMAR HUGO

CZECHOSLOVAK MATHEMATICAL JOURNAL

SPRINGER HEIDELBERG

Lugar: HEIDELBERG; Año: 2016 vol. 66 p. 193 - 204

0011-4642

In this paper we solve the initial value problem for the diusion induced bydyadic fractional derivative s in R+. First we obtain the spectral analysis of the dyadicfractional derivative operator in terms of the Haar system, which unveils a structure for theunderlying heat kernel". We show that this kernel admits an integrable and decreasingmajorant that involves the dyadic distance. This allows us to provide an estimate of themaximal operator of the diusion by the Hardy-Littlewood dyadic maximal operator. As aconsequence we obtain the pointwise convergence to the initial data.