"SATCHMO AT THE WALDORF" (Westside Theatre, 407 W. 43rd St.):...

"SATCHMO AT THE WALDORF" (Westside Theatre, 407 W. 43rd St.): John Douglas Thompson (above) stars as Louis Armstrong in this drama inspired by playwright/critic Terry Teachout's acclaimed biography. Info: Ongoing, tickets $39-$79, 212-239-6200, satchmonyc.com- LINDA WINER Credit: T. Charles Erikson

Why isn't John Douglas Thompson a very big star? The actor, who burst fully formed into a kind of Off-Broadway legend with his "Othello" in 2009, has had the occasional Broadway role. But nothing, so far, that recognizes the majestic variety of his gifts.

In Terry Teachout's engrossing character-study, "Satchmo at the Waldorf," Thompson not only plays a weakened Louis Armstrong, 69, in his dressing room during his final engagements before his fatal heart attack in 1971. But the actor also morphs, with astonishing smoothness, from Armstrong into the agent he believes betrayed him and into Miles Davis, who considered the popular artist an Uncle Tom.

The play gets a bit repetitious, but Teachout -- Armstrong biographer and theater critic of The Wall Street Journal -- gracefully weaves social and political history and Thompson makes it live.

WHAT "Satchmo at the Waldorf"

WHERE Westside Theatre, 407 W. 43rd St.

INFO $39-$79; 212-239-6200; satchmonyc.com.

BOTTOM LINE Engrossing character study.

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