In a note to clients issued Wednesday, Sterne Agee’s Shaw Wu makes the case that Apple’s (AAPL) shares, still down 8% from their recent highs, are a “compelling” buy. He offers four reasons:

• “As much success as AAPL has had,” he writes, “the company has only 4%-5% share in mobile phones and 4%-5% in PCs (12%-13% including the iPad). We believe AAPL has opportunity to double or potentially even triple its market share in these end markets over the next few years, particularly with Greater China and international as underpenetrated opportunities.”
• Apple is what he calls “the ultimate platform adoption story.” The beauty of the story, he says, “is that the company doesn’t need to win everyone over to continue success. The company just needs to continue winning a fair share of its vast end markets as more users get the AAPL advantage of ‘it just works better.'”
• Apple is one of the best ways — if not the best way — to play what he sees as three “mega trends”: 1) the mobile Internet, 2) cloud computing, and 3) consumerization of technology.
• Apple’s got a strong product release schedule going into the holiday season, including iOS 5, iCloud and a new iPhone on top of the recent release of OS X Lion and three new Macs (MacBook Air, MacBook Pro, Mac Mini).