Sharp L^p-estimates for wave equation on ax+b groups

2025/06/21 by Wang, Yunxiang, Yan, Lixin · 1 citation
#22E30 #35L20 #42B15 #43A85 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17531

Abstract

Let G be the group ℝ₊\ltimes ℝⁿ endowed with Riemannian symmetric space metric d and the right Haar measure d ρ which is of ax+b type, and L be the positive definite distinguished left invariant Laplacian on G. Let u=u(t,⋅) be the solution of u_tt+Lu=0 with initial conditions u|_t=0=f and u_t|_t=0=g. In this article we show that for a fixed t ∈\mathbb R and every 1

Citations

• Endpoint results for Fourier integral operators on noncompact symmetric spaces
• Dyadic Sets, Maximal Functions and Applications on ax+b --Groups
• Wave equation and multiplier estimates on Damek-Ricci spaces
• Boundedness from H¹ to L¹ of Riesz transforms on a Lie group of exponential growth
• Wave equation and multiplier estimates on ax+b groups
• The weak-type (1,1) of Fourier integral operators of order -(n-1)/2

Cited by

• Maximal Averages on the Affine Group G_n and applications

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