On dyadic nonlocal Schrodinger equations with Besov initial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Aimar, Hugo^1,2  Bongioanni, Bruno^1,3  Gomez, Ivana^1,2 

[1] CONICET UNL, IMAL, Santa Fe, NM, Argentina

[2] UNL, Fac Ingn Quim, Santa Fe, NM USA

[3] UNL, Fac Ingn & Ciencias Hidr, Santa Fe, NM, Argentina

关键词: Schrodinger equation;    Besov spaces;    Haar basis;    Nonlocal derivatives;   

DOI  :  10.1016/j.jmaa.2013.05.001

来源: Elsevier

【 摘 要 】

In this paper we consider the pointwise convergence to the initial data for the Schrodinger-Dirac equation i partial derivative u/partial derivative t = D(beta)u with u(x, 0) = u(0) in a dyadic Besov space. Here D-beta denotes the fractional derivative of order beta associated to the dyadic distance delta on R+. The main tools are a summability formula for the kernel of D-beta and pointwise estimates of the corresponding maximal operator in terms of the dyadic Hardy-Littlewood function and the Calderon sharp maximal operator. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free