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

Minsuk Yang

doi:10.1090/S0002-9939-2015-12523-3

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

Minsuk Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper we prove a parabolic Triebel–Lizorkin space estimate for the operator given by T^αf(t, x) = ∫^t₀ ∫_ℝ^d P^α(t − s, x − y)f(s, y)dyds, where the kernel is P^α(t, x) =∫_ℝ^d^{e2πix·ξe−t|ξ|αdξ.} The operator Tα maps from L_pF^p,q s to L^pF^p,q _s+α/p continuously. It has an application to a class of stochastic integro-differential equations of the type du = −(−Δ)_α/2udt + fdX_t.

Original language	English
Pages (from-to)	2571-2578
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2015-12523-3
Publication status	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2015-12523-3

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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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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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ER -

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

Abstract

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