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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Li, Ji¹  Wick, Brett D.² 

[1] Macquarie Univ, Dept Math, Sydney, NSW 2109, Australia

[2] Washington Univ, Dept Math, One Brookings Dr, St Louis, MO 63130 USA

关键词: Bessel operator;    Two weight inequality;    Poisson kernel;   

DOI  :  10.1016/j.jmaa.2020.124178

来源: Elsevier

【 摘 要 】

Fix lambda > 0. Consider the Bessel operator Delta(lambda) := -d(2)/dx(2) - 2 lambda/x d/dx on R+ := (0, infinity) and the harmonic conjugacy introduced by Muckenhoupt and Stein. We provide the two-weight inequality for the Poisson operator P-t([lambda]) = e(-t root Delta lambda) in this Bessel setting. In particular, we prove that for a measure mu on R-+,+(2) := (0, infinity) x (0, infinity) and sigma on R+: parallel to P-sigma([lambda])(f)parallel to(L2(R+,+2;mu)) less than or similar to parallel to f parallel to(L2(R+;sigma)), 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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