'Abajo' is an adverbe used to indicate 'place'. Its most common use implies the idea of movement. That is, it is used with verbs of movement like 'to go' (ir) or 'to walk' (andar).
Tienes que ir abajo. (You have to go downstairs.)
But 'abajo' can also imply the idea of 'location', with no movement verbs, meaning 'in a lower place'. For example:
Por favor, di a María que estoy abajo. (Please, say Mary I am downstairs.)
where the verb "estar" is not a verb of movement.
So, first thing to remember about the adverb 'abajo' is that it can be used with either verbs of movement or location.
Second, this adverb can be preceded by the following prepositions: 'de', 'desde', 'hacia', 'para' and 'por', never by the preposition 'a', as it is already included in this adverb's form.
Juan va abajo. = Right
Juan va a abajo = Wrong.
And last thing to remember: Never use the adverb 'abajo' with possesives. The right form is the adverb 'debajo' + 'de...'.
'abajo mío' = Wrong; 'debajo de mi' = Correct.
'abajo suyo' = Wrong; 'debajo de él' = Correct.
Hope this helps!
(Source: Real Academia de la Lengua Española)
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