An approach to endpoint problems in oscillatory singular integrals

Alex Iosevich; Ben Krause; Hamed Mousavi

doi:10.1007/s00209-025-03859-8

An approach to endpoint problems in oscillatory singular integrals

Alex Iosevich, Ben Krause^*, Hamed Mousavi

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from L1(R) to L1, ∞(R). The methods we use are entirely elementary, and rely only on pigeonholing and stationary phase considerations.

Original language	English
Article number	66
Number of pages	7
Journal	Mathematische Zeitschrift
Volume	311
Issue number	4
Early online date	23 Sept 2025
DOIs	https://doi.org/10.1007/s00209-025-03859-8
Publication status	E-pub ahead of print - 23 Sept 2025

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© The Author(s) 2025.

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AU - Iosevich, Alex

AU - Krause, Ben

AU - Mousavi, Hamed

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N2 - In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from L1(R) to L1, ∞(R). The methods we use are entirely elementary, and rely only on pigeonholing and stationary phase considerations.

AB - In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from L1(R) to L1, ∞(R). The methods we use are entirely elementary, and rely only on pigeonholing and stationary phase considerations.

U2 - 10.1007/s00209-025-03859-8

DO - 10.1007/s00209-025-03859-8

M3 - Article (Academic Journal)

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VL - 311

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 4

M1 - 66

ER -

An approach to endpoint problems in oscillatory singular integrals

Abstract

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