Parabolic BMO estimates for pseudo-differential operators of arbitrary order

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8 Citations (Scopus)


In this article we prove the BMO-L estimate(-δ)γ/2u BMO(Rd+1)≤N∂∂tu-A(t)uL∞(Rd+1),∀u ∈ Cc∞(Rd+1) for a wide class of pseudo-differential operators A(t) of order γ∈(0, ∞). The coefficients of A(t) are assumed to be merely measurable in time variable. As an application to the equation∂∂tu=A(t)u+f,t∈R we prove that for any u∈Cc∞(Rd+1)ut Lp(Rd+1)+(-δ)γ/2uLp(Rd+1)≤N ut - A(t)u Lp(Rd+1), where p∈(1, ∞) and the constant N is independent of u.

Original languageEnglish
Pages (from-to)557-580
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 2015 Jul 15

Bibliographical note

Funding Information:
This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1401-02 .

Publisher Copyright:
© 2015 Elsevier Inc.


  • L-estimate
  • Non-local operator
  • Parabolic BMO estimate
  • Pseudo-differential operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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