Ok, I haven't tested it but something like this would be how you do it.
// add this to mysite/_config.php
DataObject::add_extension('BlogEntry', 'CustomBlogEntry');
// put this code in mysite/code/CustomBlogEntry.php
<?php
class CustomBlogEntry extends DataObjectDecorator {
public function updateCMSFields(FieldSet &$fields) {
$fields->removeFieldFromTab('Root','LeftSidebar'));
$fields->removeFieldFromTab('Root','RightSidebar'));
}
}