Breakdown of Erlauben Sie das Lesen auf dem Smartphone?
Sie
you (formal)
lesen
to read
auf
on / to (down/up to a level)
der
who, which, that (relative pronoun; die, das)
Questions & Answers about Erlauben Sie das Lesen auf dem Smartphone?
Why is Lesen capitalized and preceded by das?
This is a nominalized infinitive. You can turn any German verb into a noun that means the act of doing that action by capitalizing its infinitive form and giving it the neuter article das. Here, the verb lesen (to read) becomes the noun das Lesen (reading).
In English we just say "reading". Do I always need to use das before a nominalized verb in German?
Usually, yes. When a nominalized infinitive is the subject or object of a sentence, German almost always requires the definite article das. While English often drops the article for gerunds (the -ing words), German keeps it: Erlauben Sie das Lesen? translates to Do you allow reading?
Why does the sentence use auf dem Smartphone instead of auf das Smartphone?
The preposition auf is a two-way preposition. It takes the dative case when answering the question where? (a static location) and the accusative case when answering to where? (a movement toward a destination). Since the reading is happening at a location rather than moving toward one, we use the dative form of the neuter noun das Smartphone, which is dem Smartphone.
How do we know that the English loanword Smartphone is neuter?