Boundedness of the Orthogonal Projection on Harmonic Fock Spaces

The main result of this paper refers to the boundedness of the orthogonal projection P-alpha : L-2(R-n, d mu(alpha)) -> H-alpha(2), n >= 2 associated to the harmonic Fock space H-alpha(2), where d mu(alpha)(x) = (pi alpha)(-n/2)e(-vertical bar x vertical bar 2/alpha) dx. We prove that the operator P-alpha is not bounded on L-p(R-n, d mu(beta)) when 0 < p < 1 and we found a necessary and sufficient condition for the boundedness when 1 <= p < infinity and n is an even integer.