Weighted L^p-spaces on nilpotent, locally compact groups

2017/09/21 by Krukowski, Mateusz
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1709.07190

Abstract

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the L^p_ω-conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the literature. In particular, we do not resort to any structural theorems for locally compact groups. Subsequently, we discuss nilpotent, locally compact groups. The climax of the paper is the proof of the L^p_ω-conjecture for these groups.

Related

• Weights of reasonable growth and their application
• L^T_p- functions on locally compact groups
• L^p-L^q multipliers on locally compact groups
• Natural proof of the characterization of relatively compact families in\n L^p-spaces on locally compact groups
• L^p-Fourier and Fourier-Stieltjes algebras for locally compact groups