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 |
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Keywords
- L-estimate
- Non-local operator
- Parabolic BMO estimate
- Pseudo-differential operator
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Parabolic BMO estimates for pseudo-differential operators of arbitrary order. / Kim, Ildoo; Kim, Kyeong Hun; Lim, Sungbin.
In: Journal of Mathematical Analysis and Applications, Vol. 427, No. 2, 15.07.2015, p. 557-580.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Parabolic BMO estimates for pseudo-differential operators of arbitrary order
AU - Kim, Ildoo
AU - Kim, Kyeong Hun
AU - Lim, Sungbin
PY - 2015/7/15
Y1 - 2015/7/15
N2 - 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.
AB - 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.
KW - L-estimate
KW - Non-local operator
KW - Parabolic BMO estimate
KW - Pseudo-differential operator
UR - http://www.scopus.com/inward/record.url?scp=84925302885&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84925302885&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2015.02.065
DO - 10.1016/j.jmaa.2015.02.065
M3 - Article
VL - 427
SP - 557
EP - 580
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -