Revisiting Riesz transforms on Heisenberg groups | Zendy

P. K. Sanjay | Zendy; Sundaram Thangavelu | Zendy

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Revisiting Riesz transforms on Heisenberg groups

Author(s) -

P. K. Sanjay,

Sundaram Thangavelu

Publication year - 2012

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/704

Subject(s) - riesz transform , heisenberg group , mathematics , hermite polynomials , m. riesz extension theorem , riesz representation theorem , laguerre polynomials , dimension (graph theory) , riesz potential , pure mathematics , group (periodic table) , order (exchange) , mathematical analysis , physics , finance , economics , quantum mechanics

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions

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