A fractal local smoothing problem for the wave equation

2025/01/22 by David Beltrán, Joris Roos, Beltran, David +5 · 2 citations
Computer Science · Engineering · #28A80 #35L05 #42B20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Elasticity and Wave Propagation #FOS: Mathematics #Image and Signal Denoising Methods

paper · pdf · doi:10.48550/arxiv.2501.12805

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any given set E⊂ [1,2], we discuss a fractal frequency-localized version of the L^p local smoothing estimates for the half-wave propagator with times in E. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of E and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal-time L²→ L^q and square function bounds, for arbitrary L² functions and general time sets. We formulate a conjecture for L^p→ L^q generalizations.

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• Problems on spherical maximal functions
• Endpoint estimates for the fractal circular maximal function and related local smoothing

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