On the Hardy--Littlewood Majorant Problem for Arithmetic Sets

Ben Krause, Mariusz Mirek, Bartosz Trojan

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The aim of this paper is to exhibit a wide class of sparse deterministic sets, B⊆N, so that lim supN→∞N−1|B∩[1,N]|=0,for which the Hardy–Littlewood majorant property holds: sup|an|≤1⁡‖∑n∈B∩[1,N]ane2πinξ‖Lp(T,dξ)≤Cp‖∑n∈B∩[1,N]e2πinξ‖Lp(T,dξ), where p≥pB is sufficiently large, the implicit constant Cp is independent of N, and the supremum is taken over all complex sequences (an:n∈N) such that |an|≤1.
Original languageEnglish
Pages (from-to)164-181
JournalJOURNAL OF FUNCTIONAL ANALYSIS
Volume271
Issue number1
DOIs
Publication statusPublished - 1 Jul 2016

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