May I ask what you do read?
I know the "May I" you used is a polite way of expressing oneself but anyway there's a Brazilian proverb that goes roughly like "asking does not offend", and personally I really don't think I would never be bothered by someone asking anything. Maybe by "do you have a two handed backhand?"
Definitely this one would offend me. How dare you even think of that? I KNOW YOU DID!!!
...aham, back to the point. I was re-heading my quoted posted and -- as it is quite common unfortunately -- when I post without calm enough to read what I write I often don't express my self well and/or miss important bits of information. My answer will show that I actually read and like quite a lot of XXth century authors -- even if predominantly from the first half of it. By the way I will restrict myself to fiction authors, which is I guess is your point.
If I would name a favorite author -- I won't -- there is a good chance I would say John Steinbeck (you guessed it, XXth century! duh!). I have no words to describe his literature. This world does not deserve him. Period.
Another author which is on my short list is Brazilian Machado de Assis, which died in the beginning of the XX century (ok, we can close our eyes and count him as XIXth century, even if he did write marvelous books in the XXth century).
Camus is a full XXth century author I like a lot. Brazilian Guimarães Rosa as well. Someone like Thomas Hardy -- who lived the whole first quarter of the XXth century is another author I like.
So I was being extremely misleading with my previous post, as those examples show.
The bulk of my favorite literature is the Russians, though. All the classical names that I don't need to repeat -- and that is heavily tilted to the XIXth century. I particularly like Turgenev, which is sometimes overlooked by the towering heights of the three-headed colossus of Dostoievski, Tolstoy and Gogol. I put him right there with those three. Another Russian I really like (who died in 1920 I guess) is Andreiev. One of my favorite books of all time is Lermontov's "A Hero of our time". He is completely XIXth century.
I like a lot of French authors, for example Stendhal and Zola, but one guy stands out for me:
Last but not least, Victor Hugo. He is another guy I could quote as being my favorite author. If I would compile my favorite quotes from "Les Miserables" it would (literally) make up for some 50 pages at least.
As you see, I am quite centered on XIX and XX centuries. So if my post made you think I liked some older stuff, I am sorry. I do read Cervantes, Sterne, (to randomly quote "older" authors), but they are more the exception than the rule (I highly recommend de Maistre's "Travel around my room" (hope this is the title in English).
And one last important observation: I really like Science Fiction, but "classic" science fiction (Stanislaw Lem, Asimov, Bradbury, a bit of Clarke, etc). I think these guys basically defined the XXth century and the beginning of this one (at least the good stuff). This is a complete XXth century phenomenon obviously.
And, there is a hard to classify author (which I think is science fiction in essence) that I love which is Kurt Vonnegut. He is so XXth century that he died in the XXIth century.
Finally, for me the best literary creation of the second part of the XXth century, by far, is Calvin and Hobbes.
Hope it clarified. Had fun compiling it. I expect a "payback" from you now!