Can the K9AY antenna be used in shortwave?

This is a loop antenna only suitable for receiving because of the low radiation resistance and its closeness to the earth. It is nothing unusual. people who do not have old books will reinvent the wheel. This is not any reflection on their imagination. They had the same inventive skill as the first person to invent it.

In general there is no magic in the world. (I am tempted to think so when fault finding a circuit or system.) You cannot beat Mother Nature at her own game.

http://www.hard-core-dx.com/nordicdx.../k9ay_orig.pdf is one description.

do you think it is not good choice for a transmit antenna?

It is a loop antenna with a circumference much shorter than a wavelength. This will put the input impedance in the few ohm region. You would be much better off with a vertical or a larger loop.

Amateur radio publications have examples of HF antennas for limited space that work best.