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.
|Original language||English (US)|
|Number of pages||37|
|Journal||Indiana University Mathematics Journal|
|State||Published - 2022|
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