【摘 要】
：
We prove weighted mixed-norm Lqt(W2x,p)and Lqt(C2x,α)estimates for 1＜p,q＜∞ and 0＜α＜1,weighted mixed weak-type estimates for q = 1,L∞t(Lpx)-BMOt(W2x,p),and L∞t(
【机 构】
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Department of Mathematics,Iowa State University,Ames,IA 50011,USA;Departamento de Matem áticas, Univ
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We prove weighted mixed-norm Lqt(W2x,p)and Lqt(C2x,α)estimates for 1＜p,q＜∞ and 0＜α＜1,weighted mixed weak-type estimates for q = 1,L∞t(Lpx)-BMOt(W2x,p),and L∞t(Cαx)-BMOt(C2x,α),and a.e.pointwise formulas for derivatives,for the solutions u = u(t,x)to parabolic equations of the form?tu-aij(t)?iju+u = f,t ∈ R,i∈Rn and for the Cauchy problem{?tv-aij(t)?ijv+v = f for t＞0,x ∈ Rn,v(0,x)= g for x ∈ Rn.The coefficients a(t)=(aij(t))are just bounded,measurable,symmetric and uniformly elliptic.Furthermore,we show strong,weak type and BMO-Sobolev estimates with parabolic Muckenhoupt weights.It is quite remarkable that most of our results are new even for the classical heat equation ?tu-△u+u = f.
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