Estimates for the full maximal function on graded Lie groups

2024/01/13 by Duván Cardona, Cardona, Duván
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.07086

openalex publication_date 2024/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On ℝⁿ, a classical result due to Bourgain establishes the restricted weak ((n)/(n-1),1) inequality for the full maximal function M_F^dσ associated to the spherical averages. In this work we present an extension to Bourgain's result on graded Lie groups for a family of full maximal operators. We formulate this extension using the group Fourier transform of the measures under consideration and the symbols of (positive Rockland operators which are) positive left-invariant hypoelliptic partial differential operators on graded Lie groups.

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