Riesz transforms on groups of Heisenberg type
نویسنده
چکیده
The aim of this article is to prove the following theorem. Theorem: Let p be in (1,∞), Hn,m a group of Heisenberg type, R the vector of the Riesz transforms on Hn,m. There exists a constant Cp independent of n and m such that for every f ∈ L (Hn,m) C p e ‖f‖Lp(Hn,m) ≤ ‖|Rf |‖Lp(Hn,m) ≤ Cpe‖f‖Lp(Hn,m). It has been proved by F. Lust-Piquard that the operator norm of R does not depend on n (see [LP]), however its behaviour in m has been entirely unknown.
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