Geoff is right, I own all the south fence and half of the west fence, the north fence is owned by my neighbour who asked me to remove the hanging pots from it. I did without argument, six months later it blew down in a storm and he asked me to go half. I will leave you to imagine my answer.
It would be better to put in some four by four posts at intervals and run trestle or wires, this will give you the freedom to hang whatever you wish on your own posts in your own ground.
Frank.