There is no such APIs in standard Java or PersonalJava, but you can use JavaPhone APIs for this purpose. They are included in the Nokia 9210 Communicator's Java implementation. You can find more information about this from the Nokia 9210 Java SDK documentation and example applications.
RE: How to send SMS messages from a Java Application?
As already answered, there currently is no generic SMS API in Java. However, if you are using Nokia 3410 phone, you can use Nokia's own SMS API, which can be found at Forum Nokia downloads.
Description for file Nokia_SMS_API_v0.9.zip:
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Nokia SMS API enables sending and receiving of GSM short messages from and to J2ME MIDP applications. The API is based on the Generic Connection Framework (javax.microedition.io package) that is used for I/O and networking functionality in the J2ME profiles. The framework has been originally specified in the Connected Limited Device Configuration specification.
The API is designed to handle messages that are text based as well as binary messages. These are represented by two subinterfaces of Message: TextMessage and BinaryMessage. These provide ways to manipulate the payload of the message as Java Strings and byte arrays, respectively.
NOTE: Nokia SMS API is supported only in Nokia 3410