Filldown with outerapply

My source data is following

    declare @dim as table
(
    name varchar(10),period int
)
insert into @dim
select * from
(
    values
        ('a', 202001),('a', 202002),('a', 202003),('a', 202004),
        ('a', 202005),('a', 202006),('a', 202007),('a', 202008),
        ('a', 202009),('a', 202010),('a', 202011),('a', 202012),
        ('b', 202001),('b', 202002),('b', 202003),('b', 202004),
        ('b', 202005),('b', 202006),('b', 202007),('b', 202008),
        ('b', 202009),('b', 202010),('b', 202011),('b', 202012)
) t (one, two)


declare @fact as table
(
    name varchar(max),period bigint,val decimal(19, 2)
)
insert into @fact
select * from
(
    values
        ('a', 202002, 100),
        ('a', 202005, 600),
        ('a', 202010, 700),
        ('b', 202004, 500),
        ('b', 202007, 600),
        ('b', 20208, 1000)
) t (one, two, three)

I was wondering if it is possible at all to achieve a fill-down inside an outer-apply. I tried as following but it did not work

select a.name,a.period,x.val, y.FD
from @dim a
outer apply (select * from @fact b where a.name=b.name and a.period=b.period) as x
outer apply (select max(x.val) over (partition by a.name order by a.period ASC ROWS UNBOUNDED PRECEDING)) as y (FD)

The reason why I am keen on achieving the fill down inside outer-apply because I can keep on utilizing that filled down column from outer-apply in the same query in succeeding apply to create further calculated columns or transformation without the help of any temp table as following

select a.name,a.period,x.val, y.FD, z.bucket
from @dim a
outer apply (select * from @fact b where a.name=b.name and a.period=b.period) as x
outer apply (successful fill down) as y (FD)
outer apply (VALUES(CASE WHEN FD>1000 then 'bucket1' else 'bucket2' end) as z(bucket)

My desired result

name	period	val	FD
a	202001	NULL	NULL
a	202002	100.00	100.00
a	202003	NULL	100.00
a	202004	NULL	100.00
a	202005	600.00	600.00
a	202006	NULL	600.00
a	202007	NULL	600.00
a	202008	NULL	600.00
a	202009	NULL	600.00
a	202010	700.00	700.00
a	202011	NULL	700.00
a	202012	NULL	700.00
b	202001	NULL	NULL
b	202002	NULL	NULL
b	202003	NULL	NULL
b	202004	500.00	500.00
b	202005	NULL	500.00
b	202006	NULL	500.00
b	202007	600.00	600.00
b	202008	NULL	600.00
b	202009	NULL	600.00
b	202010	NULL	600.00
b	202011	NULL	600.00
b	202012	NULL	600.00

Which can be achieved by following but outside of an outer-apply which I am not looking for.

select a.name,a.period,x.val, MAX(x.val) over (partition by a.name order by a.period ASC ROWS UNBOUNDED PRECEDING) as FD
from @dim a
outer apply (select * from @fact b where a.name=b.name and a.period=b.period) as x

Solution

Your problem is that you are putting the MAX window function inside an APPLY.

When you use an APPLY, the whole subquery is (logically) evaluated for each row. So the subquery, which only contains a select, only has one row, and that is evaluated per row of the outer table.

You cannot use window functions in this way. Window functions are only (logically) evaluated after joining and grouping, in the select phase and before ordering. The APPLY comes in the join phase, which is earlier.

Note that your first APPLY can be rewritten as a simple LEFT JOIN.

select
    a.name,
    a.period,
    x.val, 
    FD = max(x.val) over 
         (partition by a.name
         order by a.period ROWS UNBOUNDED PRECEDING)
from @dim a
left join @fact x on a.name = x.name and a.period = x.period

If you want the MAX to be used in other parts of the query, you must place it in a derived table.

select *,
  SomeOtherCalculationInvolvingFD
from (
  select
    a.name,
    a.period,
    x.val, 
    FD = max(x.val) over 
         (partition by a.name
         order by a.period ROWS UNBOUNDED PRECEDING)
  from @dim a
  left join @fact x on a.name = x.name and a.period = x.period
) t

I leave you with one tip: APPLY is very useful, but don't go round hammering every nail with it. Understand how it works, use appropriately.