Weighted Lp estimates for the area integral associated to self-adjoint operators

Ruming Gong, Lixin Yan*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    This article is concerned with some weighted norm inequalities for the so-called horizontal (i.e., involving time derivatives) area integrals associated to a non-negative selfadjoint operator satisfying a pointwise Gaussian estimate for its heat kernel, as well as the corresponding vertical (i.e., involving space derivatives) area integrals associated to a non-negative self-adjoint operator satisfying in addition a pointwise upper bounds for the gradient of the heat kernel. As applications, we obtain sharp estimates for the operator norm of the area integrals on Lp(Rn) as p becomes large, and the growth of the Ap constant on estimates of the area integrals on the weighted Lp spaces.

    Original languageEnglish
    Article numberA002
    Pages (from-to)25-49
    Number of pages25
    JournalManuscripta Mathematica
    Volume144
    Issue number1-2
    DOIs
    Publication statusPublished - 2013

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