Weighted hardy spaces associated with operators satisfying reinforced off-diagonal estimates

The Anh Bui, Jun Cao, Luong Dang Ky, Dachun Yang*, Sibei Yang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)

    Abstract

    Let L be a nonnegative self-adjoint operator on L2(ℝn) satisfying the reinforced (pl,p'l) off-diagonal estimates, where pl [1,2) and p'L denotes its conjugate exponent. Assume that p (0,1] and the weight w satisfies the reverse Hölder inequality of order (p'L/p)'. In particular, if the heat kernels of the semigroups {e~tL}t>0 satisfy the Gaussian upper bounds, thenpL = 1 and hence w G A00(ℝn). In this paper, the authors introduce the weighted Hardy spaces Hp L w(ℝn) associated with the operator L, via the Lusin area function associated with the heat semigroup generated by L. Characterizations of Hp L w (ℝn), in terms of the atom and the molecule, are obtained. As applications, the bounded-ness of singular integrals such as spectral multipliers, square functions and Riesz transforms on weighted Hardy spaces HL p w(ℝn) are investigated. Even for the Schrödinger operator - Δ + V with 0 < V e L1oc(ℝn), the obtained results in this paper essentially improve the known results by extending the narrow range of the weights into the whole A∞(Rn) weights.

    Original languageEnglish
    Pages (from-to)1127-1166
    Number of pages40
    JournalTaiwanese Journal of Mathematics
    Volume17
    Issue number4
    DOIs
    Publication statusPublished - 23 Jul 2013

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