Translation:You are welcome!
Is this a reply when someone thanks you, or is this a greeting telling someone they are welcome to enter a place? Or is it like in English, and can be used both ways?
This is a reply to a thank-you. A literal translation would be "heartily".
The greeting "welcome" would be a conjugation of the verb üdvözöl, depending on the numbers of greeters and greeted ones. For instance it's "Üdvözöllek" if a single person greets a single person (and they're familiar with each other).
I would suggest: ''Welcome!'' to be just as valid as: ''You are welcome!''
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Szívesen is an answer to "thank you". Is welcome alone, in itself used in that case?
Just as a shortened form, as a remnant of "You are welcome". Just like you could say "Morning" for "Good morning", and, in Hungarian, "Napot!" for "Jó napot!".
So is "You're very welcome" actually wrong, or has it just not been included as an acceptable interpretation?
The "very" might be a bit too much here. You can say "nagyon szívesen" to catch that better.
Isn't "here you are" the real meaning of it? Like bitteschön in German - thats the way I've learned it
To refer to my reply to Bianca above, the "Here you go/are/Bitteschön" meaning while giving something is rather covered by Tessék. Then you thank with Köszönöm and the proper reply to these thanks ("You're welcome/Gern geschehen") is Szívesen.
Is it also possible to say Tesèg (not sure if spelt correctly) when saying you're welcome?
Tessék. All the accent marks in Hungarian go upwards. :)
You say tessék usually when you're giving something to someone. It's more of a "Here you go!"
A possible dialogue could go like this: "Tessék." - "Nagyon köszönöm." - "Szívesen!"
That would be better translated with something like az üdvözölésed. :)
There's a grave difference between "your" and "you're". You should adhere to that when you're learning a language.
Szia minden ok nélkül is lehet hogy a héten utolsó pillanatban kívánok a továbbiakban is tudunk róla a vizet a pohárba töltjük
Üdvözöllek is a different "welcome". It's more of a "I greet you" or "I welcome you at this place", which is simply expressed with "Welcome" in English, not with "You are welcome."
"You are welcome"/szívesen is used after someone thanks you for doing something for them.