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Banach envelopes of some quasi-Banach function spaces

Kamińska A., Kubiak D.

Commentationes Mathematicae

2016

Vol 56, No. 1

87--101

We show that under some assumptions on the Musielak−Orlicz function generating a quasi-Banach Musielak−Orlicz function space, the Banach envelope of the weighted Cesàro−Musielak−Orlicz space generated by a certain positive sublinear operator is a weighted L1-space.

Landau-type theorem for variable Lebesgue spaces

Maligranda L., Wnuk W.

Commentationes Mathematicae

2015

Vol 55, No. 2

119--126

We describe, using elementary methods, the Köthe dual of variable Lebesgue spaces Lp(⋅), called also Nakano spaces, independenly for p(⋅)∈(1,∞) and p(⋅)∈(0,1). The case when p(⋅)∈[1,∞] is also included.

On the generalized Nakano sequence space

Sengonul M.

Demonstratio Mathematica

2007

Vol. 40, nr 4

885-893

The purpose of this note is to define and to investigate the generalized Nakano sequence space A(p) and to show that the sequence space A(p) eąuipped with the Luxemburg norm is rotund and posses property-H when p = (pk) is bounded with pk > 1 for all k is an element of N.