A complete search of the internet has found these results:
Hope you are doing well is the most popular phrase on the web.
These phrases have similar meanings and usages when addressing someone you haven't seen in awhile. "I hope you are doing well" is much more common, especially in letters and emails.
497,000 results on the web
Dear Louisa, I hope you are doing well.
Hope you're doing well. I'm fine here. Everything's good.
Thanks, Mike... hope you're doing well otherwise.
Hello, this is Michael. Hope you're doing well. I'm fine here. Everything's good.
Don't worry, Harriet, you are doing well indeed, for a beginner.
"I just hope he's doing well somewhere these days."
You are doing your job well.
I have heard that she hopes you are doing very well.
He said that he hopes you are doing well after your stint in the hospital.
How do you feel these days? I hope you are doing well!
234,000 results on the web
Hope you are doing fine enough for the both of us.
He says he sends his love and hopes you are doing fine these days.
Marty says he hopes the girls are doing fine.
Steve and Jim hope we are doing fine.
Thinking about Mike, Wes and Travis--hope they are doing fine.
I hope Steve is doing fine.
They had to emergency section her baby. I hope they are doing fine.
It's getting a little warm out here, but we are doing fine I hope.
No, Marianne said she hopes they are doing fine.
You are doing fine in my book.