Sentence examples for follow by using from inspiring English sources

The results of (c) and (d) follow by using similar arguments as above, and so we omit the proofs here.

The Riesz transforms occur to be Calderón Zygmund operators hence their mapping properties follow by using results from a general theory.

Proof Both statements of the theorem follow by using Lemmas 3.2, 4.10, 2.3 and 2.1.

The statements directly follow by using the identities (3.1), (3.3) and (3.4).

Finally, our conclusion will follow by using the regularity result for the elliptic transmission problem (see [11]).

The two results immediately follow by using the last two assertions of Corollary 2.6 for (u-v).

(n) The statement immediately follows by using the condition (L_{2}=1) in (23).

(r) The statement immediately follows by using the condition (L_{3}=1) in (24).

(v) The statement immediately follows by using the condition (L_{4}=1) in (25).

(j) The statement immediately follows by using the condition (L_{1}=1) in (22).

Finally, the proof of (iii) follows by using similar arguments as in the proof of (iii), Theorem 2.1.