From what I know, your best bet for writing a java  app on a pda  is
Waba, which is a "strict subset of the syntax of the Java language.
This allows developers who are familiar with Java to quickly start
programming in Waba."

"With Waba, you can write  one program that can run on a PalmPilot
device, Windows CE device or any machine that supports Java (either
the JDK 1.02, 1.1, 1.2 or 2.0)."

Also, you can use superWaba, which is waba with some additional
components, especially in the UI field.

I don't think the pda type  databases can be accesed via JDBC, but waba
has a Catalog class to access this databases.

Waba's homepage is wabasoft.com, and Superwaba's is superwaba.org

Both are free, but superwaba charges money for the tutorials.