At the share level, no. This is due to shares do not have system acl's. But you can enable auditing on the file system level for Write access to the shared folder. Refer to the following help text for the Advanced Audit Policy Configuration > Object Access:
This policy setting allows you to audit user attempts to access file system objects. A security audit event is generated only for objects that have system access control lists (SACL) specified, and only if the type of access requested, such as Write, Read, or Modify and the account making the request match the settings in the SACL. For more information about enabling object access auditing, see http://go.microsoft.com/fwlink/?LinkId=122083.
If you configure this policy setting, an audit event is generated each time an account accesses a file system object with a matching SACL. Success audits record successful attempts and Failure audits record unsuccessful attempts.
If you do not configure this policy setting, no audit event is generated when an account accesses a file system object with a matching SACL.
Note: You can set a SACL on a file system object using the Security tab in that object's Properties dialog box.
Volume: Depends on how the file system SACLs are configured.