The following sections from the Chicago Manual of Style (16th ed.) deal with these issues:
6.22 RESTRICTIVE AND NONRESTRICTIVE CLAUSES--"WHICH" VERSUS "THAT"
A relative clause is said to be restrictive if it provides information that is essential to the meaning of the sentence. Restrictive relative clauses are usually introduced by that (or who/whom/whose) and are never set off by commas from the rest of the sentence. The pronoun that may occasionally be omitted (but need not be) if the sentence is just as clear without it, as in the second example (before "I").
The version of the manuscript that the editors submitted to the publisher was well formatted.
The book I have just finished is due back tomorrow; the others can wait.
I prefer to share the road with drivers who focus on the road rather than on what they happen to be reading.
A relative clause is said to be nonrestrictive if it could be omitted without obscuring the identity of the noun to which it refers or otherwise changing the meaning of the rest of the sentence. Nonrestrictive relative clauses are usually introduced by which (or who/whom/whose) and are set off from the rest of the sentence by commas.
The final manuscript, which was well formatted, was submitted to the publisher on time.
Ulysses*, which I finished early this morning, is due back on June 16.*
I prefer to share the road with illiterate drivers, who are unlikely to read books while driving.
Although which can be substituted for that in a restrictive clause (a common practice in British English), many writers preserve the distinction between restrictive that (with no commas) and nonrestrictive which (with commas). See also 5.220 under that; which.
6.26 COMMAS WITH RESTRICTIVE AND NONRESTRICTIVE PHRASES
A phrase that is restrictive--that is, essential to the meaning (and often the identity) of the noun it belongs to--should not be set off by commas. A nonrestrictive phrase, however, should be enclosed in commas (or, if at the end of a sentence, preceded by a comma). See also 6.22.
The woman with the guitar over her shoulder is my sister.
My sister, with her guitar over her shoulder, turned to the drummer and gave the signal to begin.
6.36 COMMAS WITH INTRODUCTORY ADVERBIAL PHRASES
An introductory adverbial phrase is often set off by a comma but need not be unless misreading is likely. Shorter adverbial phrases are less likely to merit a comma than longer ones.
After reading the note, Henrietta turned pale.
On the other hand, his vices could be considered virtues.
After 1956 such complaints about poor fidelity became far less common.
Before eating, the members of the committee met in the assembly room.
To Anthony, Blake remained an enigma.
A comma should not be used if the introductory adverbial phrase immediately precedes the verb it modifies.
Before the footlights stood one of the most notorious rakes of the twenty-first century.
Restrictive vs. non-restrictive phrases is generally a very difficult concept, but the CMoS outlined it well. For your sentence, "for certain expressions" is likely a restrictive (and thereby necessary to meaning) prepositional phrase.
If you punctuate your sentence as, "We show that, for certain expressions, the usage of a comma is inevitable," then your commas imply that "for certain expressions" is non-restrictive. If you remove it from the sentence, we now have, "We show that the usage of a comma is inevitable." It simply doesn't make sense without the phrase. Therefore, we shouldn't punctuate it as a non-restrictive phrase.
However, if you punctuate the sentence as, "We show that for certain expressions, the usage of a comma is inevitable," then your comma only implies an introductory phrase for your dependent clause. "The usage of a comma is inevitable," is your dependent clause, while "We show that…" is your main clause. If you isolate the dependent clause, the introductory phrase becomes clear: For certain expressions, the usage of a comma is inevitable. Introductory phrases tend to take commas because they deviate from the order English naturally takes: subject-verb-object. As the nominative subject is not first in the sentence, a comma setting apart the introductory phrase is customary. (For short introductory phrases or single words, commas are not always necessary, but they are never incorrect.)
I hope this has helped.