I am trying to understand why Sony's PDA market share grew in the first quarter? 

Please look this article for reference:

http://rim.pdablast.com/articles/2003/4/2003429-Handheld-Sales-Down-11.html

Hi there! This is just my opinion so I entered it in the comment
section so you wouldn't be charged.

Unlike the other PDA manufacturers, Sony also sells PDA / Cellphone
hybrids and if they are included in the counting, Sony's competitors
numbers will be affected.

"With less than appealing PDAs around, some consumers have turned to
converged devices or enhanced mobile phones."

"'The Sony Ericsson P800 and O2 XDA, for example, do the job of PDAs
and function as a mobile phone', said Ma."

"Interestingly, the growth in converged devices come from them being
bought for their phone functionality rather than PDA features, he
added."

"Handheld market dips for the first time"
http://www.asiacomputerweekly.com/acw_ViewArt.cfm?Magid=1&Artid=19744&Catid=1&subcat=4