Weighted estimates for Hardy-Littlewood maximal functions on Harmonic NA groups

2023/07/20 by Pritam Ganguly, Ganguly, Pritam, Tapendu Rana +3
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2307.10806

Abstract

Our aim in this article is to study the weighted boundedness of the centered Hardy-Littlewood maximal operator in Harmonic NA groups. Following Ombrosi et al. \citeORR, we define a suitable notion of A_p weights, and for such weights, we prove the weighted L^p-boundedness of the maximal operator. Furthermore, as an endpoint case, we prove a variant of the Fefferman-Stein inequality, from which vector-valued maximal inequality has been established. We also provide various examples of weights to substantiate many aspects of our results. In particular, we have shown certain spherical functions of the Harmonic NA group constitute examples of A_p weights. The purely exponential volume growth property of the Harmonic NA group has played a crucial role in our proofs.

Related

• Weighted maximal inequalities on hyperbolic spaces
• Hardy-Littlewood maximal operator on spaces of exponential volume growth
• Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group
• Vector A₂ weights and a Hardy-Littlewood maximal function
• On the necessity of bump conditions for the two-weighted maximal inequality