Vector-valued estimates for shifted operators

2024/01/31 by Bae Jun Park, Park, Bae Jun · 2 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2401.17785

openalex publication_date 2024/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear multipliers, and multilinear rough singular integrals. Estimates for such shifted operators have a certain logarithmic growth in terms of the shift factor, but the optimality of the logarithmic growth has not yet been fully resolved. In this article, we provide sharp vector-valued shifted maximal inequality for generalized Peetre's maximal function, from which improved estimates for the above shifted operators follow with optimal logarithmic growths in a new way. We also obtain a vector-valued maximal inequality for the shifted (dyadic) Hardy-Littlewood maximal operator.

Cited by

• The Interplay of Shifted Square and Maximal Function Estimates in the Context of Multilinear Fourier Multipliers
• An alternate approach to bilinear rough singular integrals

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