In a letter, Oscar Wilde said the main characters in the novel are reflections of himself: "Basil Hallward is what I think I am: Lord Henry what the world thinks me" Doran Gray what I would like to be—in other ages, perhaps." How can you understand Oscar Wilde's view through these words?

What this extract shows is the multi-faceted nature of Wilde's personality and the enormous gap between how he was perceived by others and what he was really like.
Here was a man with a great love for humanity and a sensitivity to its sufferings. Yet, to the outside world, he came across as an aesthete and a dandy, a larger-than-life character who looked down his nose on society from his lofty intellectual heights. That's what Wilde means when he says that the world thinks of him as Lord Henry Wotton, the upper-class hedonist whose sensualist philosophy leads Dorian astray and corrupts his soul.
Wilde regards himself as much closer in personality to Basil Hallward, the sensitive artist who paints Dorian Gray's portrait. He's similar to Basil in that he's portraying a particular world rather than endorsing its values. But many readers of the story couldn't grasp this subtle distinction between showing a world full of perversion and rampant immorality and actually recommending its warped values as a way of life. They thought that Wilde was like Lord Henry, the louche aristocrat who encourages Dorian to take a walk on the wild side. They thought that The Picture of Dorian Gray was some kind of aesthete's manifesto on how to live a scandalous life.
Yet, at the same time, Wilde can't resist identifying with Dorian in some respects. As he indicates in the above letter, he would like to be like him, but in other ages. Presumably, Wilde is referring to those historical periods—Ancient Rome, perhaps?—in which such behavior as Dorian displays would've been much easier to get away with.