A300 Captain reported a hydraulic malfunction after landing gear failed to retract during initial climb. The flight returned to the departure airport and landed.

Narrative

After take off upon gear retraction we got a green system hydraulic low pressure ECAM; as well as some vibration. The landing gear failed to retract as well. I had the First Officer work the ECAM messages while I was pilot flying and ATC comm. I elected to [advise ATC] and planned to return to ZZZ. We were overweight for landing so given the nature of the situation I felt it was safe to burn fuel to be under max landing weight. All ECAM; QRH; and performance were completed during the 40 minute hold time. Dispatch was notified as well. We landed uneventfully on ZZZ XXL (XXR was closed) in a normal flaps 40 condition.I think we did a good job as a crew performing our required checklists and communications to return the aircraft to ZZZ in a safe well paced manner. I must complement ATC for very helpful and accommodating. ARFF (Airport Rescue and Firefighting) was standing by as well. The only thing that I forgot was we did not get an Amended Release for our return. We sent a message to Dispatch notifying them of our situation and used the divert function on ACARS.I dont have a suggestion on prevention but I feel our training prepared us well for this event