  In this paper, we consider a variant of the classical algorithmic problem of
checking whether a given word $v$ is a subsequence of another word $w$. More
precisely, we consider the problem of deciding, given a number $p$ (defining a
range-bound) and two words $v$ and $w$, whether there exists a factor
$w[i:i+p-1]$ (or, in other words, a range of length $p$) of $w$ having $v$ as
subsequence (i.\,e., $v$ occurs as a subsequence in the bounded range
$w[i:i+p-1]$). We give matching upper and lower quadratic bounds for the time
complexity of this problem. Further, we consider a series of algorithmic
problems in this setting, in which, for given integers $k$, $p$ and a word $w$,
we analyse the set $p$-Subseq$_{k}(w)$ of all words of length $k$ which occur
as subsequence of some factor of length $p$ of $w$. Among these, we consider
the $k$-universality problem, the $k$-equivalence problem, as well as problems
related to absent subsequences. Surprisingly, unlike the case of the classical
model of subsequences in words where such problems have efficient solutions in
general, we show that most of these problems become intractable in the new
setting when subsequences in bounded ranges are considered. Finally, we provide
an example of how some of our results can be applied to subsequence matching
problems for circular words.
