Maximal regularity of parabolic equations associated to generalized Hardy operators in weighted mixed-norm spaces

Abstract

Consider the operator on L2(Rd)La=(−Δ)α/2+a|x|−αwith0<α<min⁡{2,d}anda≥a⁎, where a⁎=−2αΓ((d+α)/4)2Γ((d−α)/4)2. In this paper we prove an weighted mixed norm inequality for the maximal regularity of the parabolic equation{ut+Lau=f,t∈[0,T)u(0,⋅)=0. The result is new and interesting even for the unweighted case.