An L q(L p)-Theory for Parabolic Pseudo-Differential Equations: Calderón-Zygmund Approach

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    Abstract

    In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators A(t) of arbitrary order γ∈ (0 , ∞). It is assumed that (t) is merely measurable with respect to the time variable. The unique solvability of the equation∂u∂t=Au−λu+f,(t,x)∈Rd+1 and the Lq(R,Lp)-estimate ∥ut∥Lq(R,Lp)+∥(−Δ)γ/2u∥Lq(R,Lp)+λ∥u∥Lq(R,Lp)≤N∥f∥Lq(R,Lp)are obtained for any λ > 0 and p, q∈ (1 , ∞).

    Original languageEnglish
    Pages (from-to)463-483
    Number of pages21
    JournalPotential Analysis
    Volume45
    Issue number3
    DOIs
    Publication statusPublished - 2016 Oct 1

    Bibliographical note

    Publisher Copyright:
    © 2016, Springer Science+Business Media Dordrecht.

    Keywords

    • Calderón-Zygmund approach
    • L(L)-estimate
    • Parabolic Pseudo-differential equations

    ASJC Scopus subject areas

    • Analysis

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