We present work on single and double quantum dots which have been defined in the two-dimensional electron gas of a freely suspended GaAs/AlGaAs heterostructure. The dots are formed either by pairs of etched constrictions or by gating electrodes and characterized in Coulomb blockade measurements. Because of their small overall dimensions the suspended dots constitute phonon cavities in which electron transport is strongly modified by electron–phonon interaction. Our measurements indicate that the emission of phonons suppresses linear transport in the Coulomb blockade regime. Upon application of a perpendicular magnetic field Coulomb blockade oscillations reemerge, as well as under nonlinear transport conditions.