The space of m-harmonic polynomials related to a Coxeter group G and a
multiplicity function m on its root system is defined as the joint kernel of the
properly gauged invariant integrals of the corresponding generalised quantum
Calogero-Moser problem. The relation between this space and the ring
of all quantum integrals of this system (which is isomorphic to the ring of
corresponding quasiinvariants) is investigated.