A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator

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Abstract

In this paper we prove a parabolic Triebel–Lizorkin space estimate for the operator given by Tαf(t, x) = ∫t0d Pα(t − s, x − y)f(s, y)dyds, where the kernel is Pα(t, x) =∫de2πix·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.

Original languageEnglish
Pages (from-to)2571-2578
Number of pages8
JournalProceedings of the American Mathematical Society
Volume143
Issue number6
DOIs
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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