(p,q)-Convexity in quasi-Banach lattices and applications

Cuartero, Bienvenido; Triana, Miguel A.

doi:10.4064/sm-84-2-113-124

Cited by 23 publications

(9 citation statements)

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“…Remark 3.4. By the convexification method ( [9,2], see also [16] for the concrete specialisation to Hardy spaces) one obtains the same result as in Corollary 3.3 for the more general Triebel-Lizorkin spaces. We can determine from the ordinal number b (k) the level and the position k of the associated interval I ,k :…”

Section: The Main Theoremmentioning

confidence: 55%

“…Müller and G. Schechtman show that any block basis of the Haar system (h I ) I∈D N with respect to the postorder, , spans spaces that are well isomorphic to p k , 1 < p = 2 < ∞. On the other hand it is easy to find block bases of the Haar system with respect to the lexicographic order (the Rademacher functions) whose span is well isomorphic to 2 k . The postorder has its origin in computer sciences (see e.g.…”

Section: Our Main Results Ismentioning

confidence: 99%

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Postorder Rearrangement Operators

Penteker

2015

Q J Math

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Section: The Main Theoremmentioning

confidence: 55%

Section: Our Main Results Ismentioning

confidence: 99%

Postorder Rearrangement Operators

Penteker

2015

Q J Math

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“…Remark 4.10: In the proof of Theorem 4.9, it is easy to check that the equivalence of (1), (5), (6) and (7) can be established in real or complex quasi-Banach lattices, which the Maurey-Pisier type theorem (see [9]) for quasi-Banach lattices.…”

Section: Proposition 44mentioning

confidence: 97%

“…. , x n in E we have Recall that the Krivine functional calculus, allows us to define the element ( n |x n | p ) 1/p in E analogously, as for Banach lattices (see [6,26,21]). The smallest constant C is called the p-convexity (resp.…”

Section: Introductionmentioning

confidence: 99%

Complex convexity and monotonicity in quasi-Banach lattices

Lee

2007

Isr. J. Math.

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In this paper we study the monotonicity and convexity properties in quasiBanach lattices. We establish relationship between uniform monotonicity, uniform C-convexity, H-and P L-convexity. We show that if the quasiBanach lattice E has α-convexity constant one for some 0 < α < ∞, then the following are equivalent: (i) E is uniformly P L-convex; (ii) E is uniformly monotone; and (iii) E is uniformly C-convex. In particular, it is shown that if E has α-convexity constant one for some 0 < α < ∞ and if E is uniformly C-convex of power type then it is uniformly Hconvex of power type. The relations between concavity, convexity and monotonicity are also shown so that the Maurey-Pisier type theorem in a quasi-Banach lattice is proved.Finally we study the lifting property of uniform P L-convexity: if E is a quasi-Köthe function space with α-convexity constant one and X is a continuously quasi-normed space, then it is shown that the quasi-normed Köthe-Bochner function space E(X) is uniformly P L-convex if and only if both E and X are uniformly P L-convex.

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“…By Proposition 2.3, it suffices to show that every weakly null sequence in X has a subsequence whose Cesàro sequence is order bounded in X. Note that X is r-convex for 1 < r < min{p, 2} [6,Proposition 1.3]. Hence, we may assume that 1 < p < 2.…”

Section: The Properties In Ri Spacesmentioning

confidence: 99%

The order-type Banach-Saks properties

Tantrawan¹,

Leung²,

Gao³

2020

Preprint

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In this paper, we investigate several "order" versions of the Banach-Saks property. In the first half of the paper, we present some general relations among these versions in the framework of Banach lattices. We also show that for a large class of Banach lattices, the order-type Banach-Saks properties are equivalent to their hereditary versions. In the second half, we study the properties in rearrangement invariant spaces and Orlicz spaces. In particular, we establish some concrete characterizations of them in these settings.

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(p,q)-Convexity in quasi-Banach lattices and applications

Cited by 23 publications

References 0 publications

Postorder Rearrangement Operators

Postorder Rearrangement Operators

Complex convexity and monotonicity in quasi-Banach lattices

The order-type Banach-Saks properties

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