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

1 Citation (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 Sep 2020

Keywords

  • Bessel operator
  • Two weight inequality
  • Poisson kernel

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