A Sharp Inequality for Martingale Transforms and the Unconditional Basis Constant of a Monotone Basis in L p (0, 1)

1992 ◽  
Vol 330 (2) ◽  
pp. 509 ◽  
Author(s):  
K. P. Choi
Keyword(s):  
Unconditional Basis ◽  
Sharp Inequality ◽  
Basis Constant ◽  
Martingale Transforms

scholarly journals On the Norm of the Beurling–Ahlfors Operator in Several Dimensions

2011 ◽  
Vol 54 (1) ◽  
pp. 113-125 ◽  
Author(s):  
Tuomas P. Hytönen
Keyword(s):  
Hilbert Space ◽  
Sharp Inequality ◽  
Exterior Algebra ◽  
Space Norm ◽  
Martingale Transforms ◽  
Image Position

AbstractThe generalized Beurling–Ahlfors operator S on Lp(ℝn; Λ), where Λ := Λ(ℝn) is the exterior algebra with its natural Hilbert space norm, satisfies the estimateThis improves on earlier results in all dimensions n ≥ 3. The proof is based on the heat extension and relies at the bottom on Burkholder's sharp inequality for martingale transforms.

scholarly journals On Basis Constants and Duality in Banach Spaces

1979 ◽  
Vol 22 (4) ◽  
pp. 459-465
Author(s):  
Leonard E. Dor
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Unconditional Basis ◽  
The Other ◽  
Other Hand ◽  
Basis Constant

AbstractEvery Banach space with a non-shrinking (unconditional) basis (Xi) can be renormed so that the biorthogonal sequence has a much smaller (unconditional) basis constant than (xi). On the other hand, if the unconditional constant of is C < 2 then the unconditional constant of (xi) is at most C/(2—C). This estimate is sharp.

scholarly journals A Sharp Inequality for Martingale Transforms

1979 ◽  
Vol 7 (5) ◽  
pp. 858-863 ◽  
Author(s):  
D. L. Burkholder
Keyword(s):  
Sharp Inequality ◽  
Martingale Transforms

Projections on Tree-Like banach Spaces

1985 ◽  
Vol 37 (5) ◽  
pp. 908-920
Author(s):  
A. D. Andrew
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Unconditional Basis ◽  
Reflexive Banach Space ◽  
Separable Space ◽  
Bounded Linear ◽  
Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

Uniqueness of unconditional basis in quasi-Banach spaces which are not sufficiently Euclidean

Positivity ◽  
2010 ◽  
Vol 14 (4) ◽  
pp. 579-584 ◽  
Author(s):  
Fernando Albiac ◽  
Camino Leránoz
Keyword(s):  
Banach Spaces ◽  
Unconditional Basis

On a Sharp Inequality Concerning the Dirichlet Integral

1985 ◽  
Vol 107 (5) ◽  
pp. 1015 ◽  
Author(s):  
S.-Y. A. Chang ◽  
D. E. Marshall
Keyword(s):  
Sharp Inequality ◽  
Dirichlet Integral

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

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