TY - JOUR
T1 - Parabolic BMO estimates for pseudo-differential operators of arbitrary order
AU - Kim, Ildoo
AU - Kim, Kyeong Hun
AU - Lim, Sungbin
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
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
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U2 - 10.1016/j.jmaa.2015.02.065
DO - 10.1016/j.jmaa.2015.02.065
M3 - Article
AN - SCOPUS:84925302885
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 -