There is no such thing as the null string. It is the empty string. This is not just being pedantic. NULL has a number of other meanings, particularly in C (where it means '\0') and SQL (where is means "unknown value").

As for your question, I generally do:

sub function1 {
    my ($arg1, $arg2) = @_;
    $arg1 = "" unless defined $arg1;
}
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If you're using 5.10 or higher, you can do:

sub function1 {
    my ($arg1, $arg2) = @_;
    $arg1 //= ""; # This is the new defined-or operator.
}
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