On a planar Pierce--Yung operator

David  Beltran; Shaoming Guo; Jonathan Hickman

On a planar Pierce--Yung operator

David Beltran, Shaoming Guo, Jonathan Hickman

School of Mathematics

Research output: Working paper

Abstract

We show that the operator
Cf(x,y):=supv∈R∣∣p.v.∫Rf(x−t,y−t2)eivt3dtt∣∣
is bounded on Lp(R2) for every 1<p<∞. This gives an affirmative answer to a question of Pierce and Yung.

Original language	English
Publisher	ArXiv
Publication status	Submitted - 10 Jul 2024

Access to Document

https://arxiv.org/abs/2407.07563

Cite this

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AU - Hickman, Jonathan

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N2 - We show that the operator Cf(x,y):=supv∈R∣∣p.v.∫Rf(x−t,y−t2)eivt3dtt∣∣ is bounded on Lp(R2) for every 1

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