You can do it like this:
Choose the partition in which you want to apply exponential decay, then order descending by date within such a group.
use the function ROW_NUMBER() with ascendent ordering to get the row numbering within each subgroup.
calculate pow(your_variable_in_[0,1], rownum) and apply it to your result.
Code might look like this (might work in Oracle SQL or db2):
SELECT <your_partitioning>, date, <whatever>*power(<your_variable>,rownum-1)
FROM (SELECT a.*
, ROW_NUMBER() OVER (PARTITION BY <your_partitioning> ORDER BY a.date DESC) AS rownum
FROM YOUR_TABLE a)
ORDER BY <your_partitioning>, date DESC
EDIT: I read again over your problem and think I understood now what you asked for, so here is a solution which might work (decay factor is 0.9 here):
SELECT product, sum(adjusted_views) // (i)
FROM (SELECT product, views*power(0.9, rownum-1) AS adjusted_views, date, rownum // (ii)
FROM (SELECT product, views, date // (iii)
, ROW_NUMBER() OVER (PARTITION BY product ORDER BY a.date DESC) AS rownum
FROM YOUR_TABLE a)
ORDER BY product, date DESC)
GROUP BY product
The inner select statement (iii) creates a temporary table that might look like this
product views date rownum
--------------------------------------------------
a 1 2014-05-15 1
a 2 2014-05-14 2
a 2 2014-05-13 3
b 2 2014-05-10 1
b 3 2014-05-09 2
b 2 2014-05-08 3
b 1 2014-05-07 4
The next query (ii) then uses the rownumber to construct an exponentially decaying factor 0.9^(rownum-1) and applies it to views. The result is
product adjusted_views date rownum
--------------------------------------------------
a 1 * 0.9^0 2014-05-15 1
a 2 * 0.9^1 2014-05-14 2
a 2 * 0.9^2 2014-05-13 3
b 2 * 0.9^0 2014-05-10 1
b 3 * 0.9^1 2014-05-09 2
b 2 * 0.9^2 2014-05-08 3
b 1 * 0.9^3 2014-05-07 4
In a last step (the outer query) the adjusted views are summed up, as this seems to be the quantity you are interested in.
Note, however, that in order to be consistent there should be regular distances between the dates, e.g., always on day (--not one day here and a month there, because these will be weighted in a similar fashion although they shouldn't).