Abstract
In this article we prove the BMO-L∞ estimate(-δ)γ/2u BMO(Rd+1)≤N∂∂tu-A(t)uL∞(Rd+1),∀u ∈ Cc∞(Rd+1) for a wide class of pseudo-differential operators A(t) of order γ∈(0, ∞). The coefficients of A(t) are assumed to be merely measurable in time variable. As an application to the equation∂∂tu=A(t)u+f,t∈R we prove that for any u∈Cc∞(Rd+1)ut Lp(Rd+1)+(-δ)γ/2uLp(Rd+1)≤N ut - A(t)u Lp(Rd+1), where p∈(1, ∞) and the constant N is independent of u.
| Original language | English |
|---|---|
| Pages (from-to) | 557-580 |
| Number of pages | 24 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 427 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2015 Jul 15 |
Bibliographical note
Funding Information:This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02 .
Publisher Copyright:
© 2015 Elsevier Inc.
Keywords
- L-estimate
- Non-local operator
- Parabolic BMO estimate
- Pseudo-differential operator
ASJC Scopus subject areas
- Analysis
- Applied Mathematics