Multiparameter singular integrals on the Heisenberg group: uniform estimates

Marco Vitturi, James Wright

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg convolution is replaced by euclidean convolution, is that the operators on the Heisenberg group are always $L^2$ bounded. This is not the case in the euclidean setting where $L^2$ boundedness depends on the polynomial defining the underlying surface. Here we uncover some new, interesting phenomena. For example, although the Heisenberg group operators are always $L^2$ bounded, the bounds are {\it not} uniform in the coefficients of polynomials with fixed degree. When we ask for which polynoimals uniform $L^2$ bounds hold, we arrive at the {\it same} class where uniform bounds hold in the euclidean case.
Original languageEnglish
Pages (from-to)5439-5465
Number of pages24
JournalTransactions of the American Mathematical Society
Early online date26 May 2020
DOIs
Publication statusE-pub ahead of print - 26 May 2020

Keywords / Materials (for Non-textual outputs)

  • math.CA
  • 42B15, 42B20, 43A30, 43A80

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