Parabolic BMO estimates for pseudo-differential operators of arbitrary order

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Kim, Ildoo¹  Kim, Kyeong-Hun¹  Lim, Sungbin¹ 

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

关键词: Parabolic BMO estimate;    L-p-estimate;    Pseudo-differential operator;    Non-local operator;   

DOI  :  10.1016/j.jmaa.2015.02.065

来源: Elsevier

【 摘 要 】

In this article we prove the BMO-L-infinity estimate parallel to(-Delta)(gamma/2)u parallel to(BMO(Rd+1)<=) N parallel to partial derivative/partial derivative tu - A(t) u parallel to(L infinity (Rd+1)), for all u is an element of C-G(infinity) (Rd+1) for a wide class of pseudo-differential operators A(1) of order gamma is an element of (0, infinity). The coefficients of A(t) are assumed to be merely measurable in time variable. As an application to the equation partial derivative/partial derivative t u=A(t) u +f, t is an element of R we prove that for any u is an element of C-G(infinity) (Rd+1) parallel to u(t)parallel to(Lp)(Rd+1) + parallel to(-Delta)(gamma/2) u parallel to L-p(Rd+1)<= N parallel to u(t) - A(t)u parallel to L-p(Rd+1), where p is an element of (1, infinity) and the constant N is independent of u. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free