I hope things are getting better for you (life in general) = (if the things were bad) Надеюсь, ваши дела идут на поправку.
(if the things were good) Надеюсь, ваши дела идут в гору.
(more colloquial sentences)
don't be upset with me (I hope you don't mind, but...) = Не обижайся на меня, но... Надеюсь, ты не обидишься, но...