TY - JOUR
T1 - An L q(L p)-Theory for Parabolic Pseudo-Differential Equations
T2 - Calderón-Zygmund Approach
AU - Kim, Ildoo
AU - Lim, Sungbin
AU - Kim, Kyeong Hun
N1 - Funding Information:
This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02
Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators A(t) of arbitrary order γ∈ (0 , ∞). It is assumed that (t) is merely measurable with respect to the time variable. The unique solvability of the equation∂u∂t=Au−λu+f,(t,x)∈Rd+1 and the Lq(R,Lp)-estimate ∥ut∥Lq(R,Lp)+∥(−Δ)γ/2u∥Lq(R,Lp)+λ∥u∥Lq(R,Lp)≤N∥f∥Lq(R,Lp)are obtained for any λ > 0 and p, q∈ (1 , ∞).
AB - In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators A(t) of arbitrary order γ∈ (0 , ∞). It is assumed that (t) is merely measurable with respect to the time variable. The unique solvability of the equation∂u∂t=Au−λu+f,(t,x)∈Rd+1 and the Lq(R,Lp)-estimate ∥ut∥Lq(R,Lp)+∥(−Δ)γ/2u∥Lq(R,Lp)+λ∥u∥Lq(R,Lp)≤N∥f∥Lq(R,Lp)are obtained for any λ > 0 and p, q∈ (1 , ∞).
KW - Calderón-Zygmund approach
KW - L(L)-estimate
KW - Parabolic Pseudo-differential equations
UR - http://www.scopus.com/inward/record.url?scp=84962257581&partnerID=8YFLogxK
U2 - 10.1007/s11118-016-9552-3
DO - 10.1007/s11118-016-9552-3
M3 - Article
AN - SCOPUS:84962257581
SN - 0926-2601
VL - 45
SP - 463
EP - 483
JO - Potential Analysis
JF - Potential Analysis
IS - 3
ER -