一番よく使われている表現はHope you are doing wellです。
この２つの表現は長いこと会っていなかった人と話すときに同じような意味、使い方で使用される表現です。 "I hope you are doing well"は手紙やメールでよりよく使われる表現です。
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!
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.