Best Constants for the Inequalities between Equivalent Norms in Orlicz Spaces

2011 ◽  
Vol 59 (2) ◽  
pp. 165-174
Author(s):  
Ha Huy Bang ◽  
Nguyen Van Hoang ◽  
Vu Nhat Huy
Keyword(s):  
Orlicz Spaces ◽  
Best Constants ◽  
Equivalent Norms

SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

2010 ◽  
Vol 88 (1) ◽  
pp. 19-27 ◽  
Author(s):  
SORINA BARZA ◽  
JAVIER SORIA
Keyword(s):  
Lorentz Space ◽  
Lorentz Spaces ◽  
Best Constants ◽  
Sharp Constants ◽  
Dual Norm ◽  
Equivalent Norms ◽  
Weighted Lorentz Spaces ◽  
Weighted Lorentz Space

AbstractFor an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

Smooth Norms in Orlicz Spaces

1991 ◽  
Vol 34 (1) ◽  
pp. 74-82 ◽  
Author(s):  
R. P. Maleev ◽  
S. L. Troyanski
Keyword(s):  
Orlicz Spaces ◽  
Equivalent Norm ◽  
Equivalent Norms ◽  
Fréchet Differentiability ◽  
Frechet Differentiability ◽  
Fréchet Differentiable

AbstractEquivalent norms with best order of Frechet and uniformly Frechet differentiability in Orlicz spaces are constructed. Classes of Orlicz which admit infinitely many times Frechet differentiable equivalent norm are found.

scholarly journals Best Constants between Equivalent Norms in Lorentz Sequence Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
S. Barza ◽  
A. N. Marcoci ◽  
L. E. Persson
Keyword(s):  
Triangle Inequality ◽  
Sequence Spaces ◽  
Best Constants ◽  
Crucial Point ◽  
Dual Norm ◽  
Best Constant ◽  
Equivalent Norms ◽  
Level Sequence

We find the best constants in inequalities relating the standard norm, the dual norm, and the norm∥x∥(p,s):=inf⁡{∑k∥x(k)∥p,s}, where the infimum is taken over all finite representationsx=∑kx(k)in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.

Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

2020 ◽  
Vol 72 (2) ◽  
pp. 235-259
Author(s):  
Lech Maligranda ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integrals ◽  
Orlicz Spaces

Martingale Rransforms between Hardy-Orlicz Spaces of LΦPredictable Martingales

2012 ◽  
Vol 14 (3) ◽  
pp. 245
Author(s):  
Feng LUO ◽  
Lin YU ◽  
Hongping GUO
Keyword(s):  
Orlicz Spaces

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

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