Near to my room there is a frying pan and I don't know who is the owner of this kitchen utensil. What is the correct way to ask it briefly?
Whose this frying pan (is this correct?)
Whose this frying pan belongs?
You could ask:
Who owns this frying pan?
Who does this frying pan belong to?
Who is the owner of this frying pan?
Whose frying pan is this?
"Whose frying pan is this?" is how most people would say it.
Edit--"Who does this frying pan belong to?" might be about as common. "Whom" is almost never used in spoken English. (For example, you would likely have to watch many hours of television before hearing a single "whom.")
"Whom does this frying pan belong to?" seems wrong to me.
"To whom does this frying pan belong?" sounds better,
although I'd say "Whose is this frying pan?"
Although the previous answers are all fine, for me it depends on the social situation and if you're asking verbally or not, the previous answers "sound" as if they are in a written context (which I guess would fit the situation in the question if you were leaving a note).
For example if you know the other person well, they are in the same room as you, and can communicate visually by raising the pan during the question I would say this, with a raising intonation at the end of the question...
"Is this your pan?"
...or if you know them really well, simply...
This may not be linguistically or grammatically perfect, but it's the way people talk "round my way" :)