You can get the current weekday from localtime(), and it isn't hard to go backwards and forwards from there to the start / end of the week.

Code to follow...

use strict;
use warnings;

my $t = time(); $t -= $t % 86400;
my $wday = (localtime($t))[6];
my $s = $t - 86400 * $wday;
my $e = $t + 86400 * (7 - $wday) - 1;
@_ = localtime($s); $_[4]++; $_[5] += 1900;
print "$_[4]-$_[3]-$_[5] to ";
@_ = localtime($e); $_[4]++; $_[5] += 1900;
print "$_[4]-$_[3]-$_[5]";
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EDIT: Changed code slightly so $s and $e have the min timestamp on the first day and the max timestamp on the last day, respectively. You can now use them to check if a timestamp is inside the range.