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.
[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 language | English |
|---|---|
| Article number | 124178 |
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 489 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Sept 2020 |
Keywords
- Bessel operator
- Two weight inequality
- Poisson kernel