Geodesic
Maximum Modulus Theorems and Schwarz Lemmata for Sequence Spaces, II
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 79-84

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In this note, we continue the investigations of [3], proving another analogue of the maximum modulus theorem, this time for the sequence space bv, and we investigate maximal functions for such theorems. As in [3], we use the notation f∈MM if f is analytic in the disk |z| <1, continuous for |z| ≤ 1 and satisfies |f(z)| ≤ 1 on |z| = 1. We also write f∈SL if f∈MM and f(0) = 0. Whenever x={xk} is a sequence of complex numbers, we write f(x) = {f(xk)}.In [3], we proved analogues of the maximum modulus theorem for the sequence spaces 5, m and c, and analogues of the Schwarz Lemma for the sequence spaces c0, lp and bv0 . We begin this note with the sequence space bv. 
Shawyer, B. L. R. Maximum Modulus Theorems and Schwarz Lemmata for Sequence Spaces, II. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 79-84. doi: 10.4153/CMB-1978-012-6
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     title = {Maximum {Modulus} {Theorems} and {Schwarz} {Lemmata} for {Sequence} {Spaces,} {II}},
     journal = {Canadian mathematical bulletin},
     pages = {79--84},
     year = {1978},
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     doi = {10.4153/CMB-1978-012-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-012-6/}
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