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

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 Jan 1

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Fractional Laplacian
Triebel-Lizorkin Space
Integrodifferential equations
Operator
Integro-differential Equation
Estimate
Stochastic Equations
kernel
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "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.",
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A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator. / Yang, Minsuk.

In: Proceedings of the American Mathematical Society, Vol. 143, No. 6, 01.01.2015, p. 2571-2578.

Research output: Contribution to journalArticle

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AB - 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.

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