Lp Regularity for a Class of Averaging Operators on the Heisenberg Group

Geoffrey Bentsen

doi:10.1512/iumj.2022.71.8914

L^p Regularity for a Class of Averaging Operators on the Heisenberg Group

Geoffrey Bentsen^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove L^pcomp(R³) → L^p_s (R³) boundedness for averaging operators associated with a class of curves in the Heisenberg group H¹ via L² estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all L^p functions boundedly.

Original language	English (US)
Pages (from-to)	819-855
Number of pages	37
Journal	Indiana University Mathematics Journal
Volume	71
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2022.71.8914
State	Published - 2022

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Mathematics(all)

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10.1512/iumj.2022.71.8914

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abstract = "We prove Lpcomp(R3) → Lps (R3) boundedness for averaging operators associated with a class of curves in the Heisenberg group H1 via L2 estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all Lp functions boundedly.",

author = "Geoffrey Bentsen",

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N2 - We prove Lpcomp(R3) → Lps (R3) boundedness for averaging operators associated with a class of curves in the Heisenberg group H1 via L2 estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all Lp functions boundedly.

AB - We prove Lpcomp(R3) → Lps (R3) boundedness for averaging operators associated with a class of curves in the Heisenberg group H1 via L2 estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all Lp functions boundedly.

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L^p Regularity for a Class of Averaging Operators on the Heisenberg Group

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