The two-weight inequality for the Poisson operator in the Bessel setting

Ji Li*, Brett D. Wick

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Fix λ > 0. Consider the Bessel operator Δλ := -d2/dx2 - 2 λ/x d/dx on R+ := (0,∞) and the harmonic conjugacy introduced by Muckenhoupt and Stein. We provide the two-weight inequality for the Poisson operator Pt[λ] = e-t√Δλ  in this Bessel setting. In particular, we prove that for a measure μ on R2+,+ := (0,∞) x (0,∞) and σ on R+:

    [formula presents]

    if and only if testing conditions hold for the Poisson operator and its adjoint. Further, the norm of the operator is shown to be equivalent to the best constant in the testing conditions.
    Original languageEnglish
    Article number124178
    Pages (from-to)1-15
    Number of pages15
    JournalJournal of Mathematical Analysis and Applications
    Volume489
    Issue number2
    DOIs
    Publication statusPublished - 15 Sept 2020

    Keywords

    • Bessel operator
    • Two weight inequality
    • Poisson kernel

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