1. Introduction We are going to investigate the equation ut(t, x ... - ICMS

16(iii) Let µ ≤ γ and q ≥ p be such thatγ − d/p = µ − d/q.Denoteτ = θq/p(so that τ/q = θ/p). Then for any u ∈ H γ p,θwe haveu ∈ H µ q,τ, ||u|| Hµq,τ≤ N||u|| Hγp,θ .(iv) Assume γp > d and represent γ − d/p as k + ε, where k is aninteger and ε ∈ (0, 1]. Leti, j be multi–indices such that |i| ≤k, |j| = k.Then for any u ∈ H γ p,θ ,wehaveM |i|+θ/p D i u ∈ C(R d +), M k+ε+θ/p D j u ∈C ε loc(R d +),||M |i|+θ/p D i u|| C(Rd+ ) ≤ N||u|| γ,p,θ ,[M k+ε+θ/p D j u] Cε (R d +) ≤ N||u|| γ,p,θ ,where C ε (R d + ) is the Zygmund space (coinciding with Cε (R d + ) if ε ∈ (0, 1)).