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

Keywords

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

ASJC Scopus subject areas

  • Analysis

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