First: even if your accountid doesn't change it is better to use prepared statements.

    my $sql = "SELECT o.objectid, 
                   <other fields>
        FROM       object o
        WHERE       o.accountid = ?
        ORDER BY o.objectname
        LIMIT 20 OFFSET 0";

     ....

     my $sth=$dbh->prepare($sql);
     $sth->execute($accountid);
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This will give you (maybe) a small speed increase in this example.

Second: fetchall_arrayref returns all data in one structure. This involves a lot of copying. Probably you should take a look at fetchrow_arrayref. This will get one row at a time (so you can process one row at a time).