This paper examines the binary Fresnel zone plate (FZP) lens frequency-harmonic and space-resolution focusing, and its application as a FZP lens antenna. A microwave FZP lens antenna (FZPA) radiates both at design (90 GHz) and terahertz (THz) odd harmonic frequencies. Frequency and space domain antenna operation are studied analytically by use of the vector diffraction integral applied to a realistic printed FZPA. It is found that all harmonic gain peaks are roughly identical in form, bandwidth, and top values. At each harmonic frequency, the FZPA has a beamwidth that closely follows the Rayleigh resolution criterion. If the lens/antenna resolution is of prime importance and the small aperture efficiency is a secondary problem the microwave-design FZP lens antenna can be of great use at much higher terahertz frequencies. Important feature of the microwave FZP lens is its broader-zone construction compared to the equal in resolution terahertz-design FZP lens. Thus, unique and expensive microtechnology for the microwave FZP lens fabrication is not required. High-order harmonic operation of the FZP lens or lens antenna could find space resolution and frequency filtering applications in the terahertz and optical metrology, imaging tomography, short-range communications, spectral analysis, synchrotron facilities, and so on.