Muckenhoupt-Type Weights in Bessel Setting
Journal
The Journal of Geometric Analysis
Journal Volume
34
Journal Issue
7
ISSN
1050-6926
1559-002X
Date Issued
2024-04-25
Author(s)
Abstract
Fix λ>-1/2 and λ≠0. Consider the Bessel operator (introduced by Muckenhoupt–Stein) ▵λ:=-d2dx2-2λxddx on R+:=(0,∞) with dmλ(x):=x2λdx and dx the Lebesgue measure on R+. In this paper, we study the Muckenhoupt-type weights in this Bessel setting along the line of Muckenhoupt–Stein and Andersen–Kerman. Besides, exploiting more properties of the weights Ap,λ introduced by Andersen–Kerman, we introduce a new class A~p,λ such that the Hardy–Littlewood maximal function is bounded on the weighted Lwp space if and only if w is in A~p,λ. Moreover, along the line of Coifman–Rochberg–Weiss, we investigate the commutator [b,Rλ] with Rλ:=ddx(▵λ)-12 to be the Bessel Riesz transform. We show that for w∈Ap,λ, the commutator [b,Rλ] is bounded on weighted Lwp if and only if b is in the BMO space associated with ▵λ.
Publisher
Springer Science and Business Media LLC
Type
journal article