Hi,
HikaShop might not be the only incriminated component ; as you can see with your error message, the problem come from the Joomla library. So it is difficult to know what happen before.
You might have some modules which require some memory, you might have some image processing (memory depends on the image size), etc.
So, there is no specific memory requirements with HikaShop ; it really depends on what you are loading and what you are processing in your pages.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.