Ask after: preguntar por (salud).To ask for information about someone, especially about their health.Tell your father I was asking after him.I run into your old friends Vichi and Peter yesterday, they asked after you.
Ask for: solicitar.To say that you would like to see or speak to someone:A young man was here asking for you this morning.He wrote asking for help.There´s someone asking for you at reception.If you say you couldn´t ask for someone or something better, you mean that that person or thing is the best of their type:She is great to work for, I really couldn´t ask for a better boss.