Funambol, now billing itself as the leader in mobile sync, has bought Zapatec, which creates Web 2.0 solutions using AJAX.

The result, the company believes, will be a one-stop shop for building mobile applications that run as well as native apps across multiple platforms.

Funambol has its developers in Italy, Zapatec in the Ukraine, but both have operations in Silicon Valley that will be consolidated in Redwood City. Zapatec CEO Dror Matalon will become vice president of emerging technologies for the combined company, said Funambol vice president of worldwide marketing Hal Steger.

The combined company is focused on a tough problem for mobile developers, namely how do you create apps that integrate with native apps, yet don’t have to be completely rewritten for each platform.

Steger said Funambol’s sync technology solves part of the first problem, Zapatec most of the second, and the combination will enable a total solution.

“A lot of people think the future of mobile apps will be like Web apps, like AJAX apps on desktop browsers,” said Steger. “If you can build a W