Abstract
The objective of this paper is to present an estimate bounding the L 2 {L_2} -norm of a function over a bounded subset of R n {R^n} by the L 2 {L_2} -norms of its derivatives of arbitrary order over all of R n {R^n} and the L 2 {L_2} -norm of its projection onto a finite-dimensional space of functions with bounded support. The estimate essentially generalizes inequalities of Friedrichs [1, p. 284] and Lax and Phillips [2, p. 95]. An application of the estimate is made to the Fredholm theory of elliptic partial differential operators in R n {R^n} .
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