It would be nice to create a pub/sub push subscription, which pushes to Azure Event Hub. I ran into the same problem when configuring this setup.
Pub/sub push subscriptions currently do not support custom Authorization headers, which are needed as per the Event Hub documentation.
POST https://your-namespace.servicebus.windows.net/your-event-hub/messages?timeout=60&api-version=2014-01 HTTP/1.1
Authorization: SharedAccessSignature sr=your-namespace.servicebus.windows.net&sig=your-sas-key&se=1403736877&skn=RootManageSharedAccessKey
Content-Type: application/atom+xml;type=entry;charset=utf-8
Host: your-namespace.servicebus.windows.net
{ "DeviceId":"dev-01", "Temperature":"37.0" }
So the only two options I see here:
Push setup: Create a cloud function or dataflow job in Google Cloud. Push pub/sub events to this endpoint and then pass on the event to Azure Event hub with the appropriate headers.
Pull setup: Poll a pub/sub pull subscription from the Azure side with an Azure function or WebJob.
Both options require extra compute resources, so definitely not the preferred way of doing this. I would always try a push setup first, since then you don't have t o continuously have a polling job running in the background.
I have hopes that pub/sub push subscriptions will support custom headers anywhere in the future. Lately some other useful features have been added like: Dead Lettering, Message Ordering and Partitioning (Lite Topics). Hopefully they will add custom headers as well.