Hi,
There is no "inbox" system in HikaMarket (nor in HikaShop) ; but you can have a "contact" button for the vendors and the products.
The contact form will allow the user to send a message to the vendor.
There is also an option in HikaMarket to handle the "product contact" and send the HikaShop emails to the vendors instead of the store admin.
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.