On L^p-improving bounds for maximal operators associated with curves of finite type in the plane

2023/03/06 by Wenjuan Li, Li, Wenjuan, Huiju Wang +1
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2303.02897

openalex publication_date 2023/03/06 · openalex created_date 2023/03/09 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the L^p-improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set E ⊂ [1,2]. The L^p-improving region depends on the order of finite type and the fractal dimension of E. In particular, various impacts of non-isotropic dilations are also considered.

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