In this paper we prove a parabolic Triebel–Lizorkin space estimate for the operator given by Tαf(t, x) = ∫t0 ∫ℝd Pα(t − s, x − y)f(s, y)dyds, where the kernel is Pα(t, x) =∫ℝde2πix·ξe−t|ξ|αdξ. The operator Tα maps from LpFp,q s to LpFp,q s+α/p continuously. It has an application to a class of stochastic integro-differential equations of the type du = −(−Δ)α/2udt + fdXt.
All Science Journal Classification (ASJC) codes
- Applied Mathematics