A Cauchy problem for elliptic invariant differential operators and continuity of a generalized Berezin transform

ORSTED BENT, VARGAS JORGE

ANNALES DE L INSTITUT FOURIER

Annals de L'Institut Fourier

Lugar: Grenoble; Año: 2007 vol. 57 p. 693 - 702

0373-0956

In this note, wegeneralize the results in our previous paper cite{ov}, by showing the $(L^2,L^2)-$continuity of ageneralized Berezin transform associated with a branching problem for a class of unitary representationsdefined by invariant elliptic operators;  we also show, that under suitable general conditions,  thisgeneralized Berezin transform is $(L^p, L^p)-$continuous for $ 1 leq p leq infty.$