Pointwise convergence to the initial data for nonlocal dyadic diffusions

Title:

Pointwise convergence to the initial data for nonlocal dyadic diffusions

Creator:

Actis, Marcelo and Aimar, Hugo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:63d8c767-6e1d-4342-9403-398730a184ac
uuid:63d8c767-6e1d-4342-9403-398730a184ac
issn:0011-4642

Subject:

matematika, konvergence řady, mathematics, convergence of series, pointwise convergence, nonlocal diffusion, dyadic fractional derivatives, Haar base, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We solve the initial value problem for the diffusion induced by dyadic fractional derivative s in \mathbb{R}^{+}. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data., Marcelo Actis, Hugo Aimar., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

193-204

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:1

Harvested from:

CDK

Metadata only:

false