Abstract:
We obtain upper and lower estimates for ɛ-entropy and entropy numbers of multiplier operators of systems of orthonormal functions bounded from Lp to Lq. Upper estimates in our study require that a Marcinkiewicz-type multiplier theorem is available for the system. As application we obtain estimates for ɛ-entropy and entropy numbers of the multiplier operators associated with the sequences (k−γlnk−ξ)k=2∞ and (e−γk)k=0∞ where γ>0, ξ≥0 and 0[removed]