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Rademacher functions in Cesàro type spaces

100%

Astashkin S., Maligranda L.

Studia Mathematica

2010

tom 198

nr 3

235-247

The Rademacher sums are investigated in the Cesàro spaces $Ces_{p}$ (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces $K_{p,w}$ on [0,1]. They span l₂ space in $Ces_{p}$ for any 1 ≤ p < ∞ and in $K_{p,w}$ if and only if the weight w is larger than $t log₂^{p/2}(2/t)$ on (0,1). Moreover, the span of the Rademachers is not complemented in $Ces_{p}$ for any 1 ≤ p < ∞ or in $K_{1,w}$ for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is a complemented subspace in $K_{p,w}$.

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

81%

Astashkin S., Hernández F., Semenov E.

Studia Mathematica

2009

tom 193

nr 3

269-283

If G is the closure of $L_{∞}$ in exp L₂, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular and E ⊊ G. For any Marcinkiewicz space M(φ) ⊂ G such that M(φ) is not an interpolation space between $L_{∞}$ and G it is proved that there exists another Marcinkiewicz space M(ψ) ⊊ M(φ) with the property that the M(ψ) and M(φ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.

Ograniczanie wyników

2 Studia Mathematica

2 Astashkin S.

1 Hernández F.

1 Maligranda L.

1 Semenov E.

1 2010

1 2009

Wyniki wyszukiwania

Rademacher functions in Cesàro type spaces

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces