Optimal constants in non-commutative Hölder inequality for quasi-norms

2020 ◽  
pp. 1
Author(s):  
F. Sukochev ◽  
D. Zanin
Keyword(s):  
Hölder Inequality ◽  
Optimal Constants

scholarly journals New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 227 ◽  
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du ◽  
Yasong Chen
Keyword(s):  
Invariant Subspace ◽  
Type Inequality ◽  
Invariant Subspaces ◽  
Minkowski Inequality ◽  
Hölder Inequality ◽  
Stability Theorem ◽  
Mixed Norm ◽  
Lebesgue Spaces

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

The reverse Hölder inequality for power means

2012 ◽  
Vol 183 (6) ◽  
pp. 762-771
Author(s):  
Viktor D. Didenko ◽  
Anatolii A. Korenovskyi
Keyword(s):  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Power Means ◽  
Reverse Hölder

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

Optimal Constants in the Khintchine Type Inequalities

2020 ◽  
pp. 135-161
Author(s):  
Sergey V. Astashkin
Keyword(s):  
Optimal Constants

scholarly journals Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates

2013 ◽  
Vol 1 ◽  
pp. 69-129 ◽  
Author(s):  
The Anh Bui ◽  
Jun Cao ◽  
Luong Dang Ky ◽  
Dachun Yang ◽  
Sibei Yang
Keyword(s):  
Hardy Space ◽  
Orlicz Function ◽  
Riesz Transform ◽  
Hölder Inequality ◽  
Muckenhoupt Weights ◽  
Order Elliptic Operator ◽  
Lusin Area Function ◽  
Reverse Hölder ◽  
Conjugate Exponent

Abstract Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order (qL/l(φ))′, where (qL/l(φ))′ denotes the conjugate exponent of qL/l(φ). In this paper, the authors introduce a Musielak-Orlicz-Hardy space Hφ;L(X), via the Lusin-area function associated with L, and establish its molecular characterization. In particular, when L is nonnegative self-adjoint and satisfies the Davies-Gaffney estimates, the atomic characterization of Hφ,L(X) is also obtained. Furthermore, a sufficient condition for the equivalence between Hφ,L(ℝn) and the classical Musielak-Orlicz-Hardy space Hv(ℝn) is given. Moreover, for the Musielak-Orlicz-Hardy space Hφ,L(ℝn) associated with the second order elliptic operator in divergence form on ℝn or the Schrödinger operator L := −Δ + V with 0 ≤ V ∊ L1loc(ℝn), the authors further obtain its several equivalent characterizations in terms of various non-tangential and radial maximal functions; finally, the authors show that the Riesz transform ∇L−1/2 is bounded from Hφ,L(ℝn) to the Musielak-Orlicz space Lφ(ℝn) when i(φ) ∊ (0; 1], from Hφ,L(ℝn) to Hφ(ℝn) when i(φ) ∊ (; 1], and from Hφ,L(ℝn) to the weak Musielak-Orlicz-Hardy space WHφ(ℝn) when i(φ)=is attainable and φ(·; t) ∊ A1(X), where i(φ) denotes the uniformly critical lower type index of φ

scholarly journals Variants of the Hölder Inequality and its Inverses

1977 ◽  
Vol 20 (3) ◽  
pp. 377-384 ◽  
Author(s):  
Chung-Lie Wang
Keyword(s):  
Hölder Inequality ◽  
Real Numbers

AbstractThis paper presents variants of the Holder inequality for integrals of functions (as well as for sums of real numbers) and its inverses. In these contexts, all possible transliterations and some extensions to more than two functions are also mentioned.

Estimates for $$\bar{\partial }$$ and Optimal Constants

2015 ◽  
pp. 45-50 ◽  
Author(s):  
Zbigniew Błocki
Keyword(s):  
Optimal Constants

THE MAIN INEQUALITY OF 3D VECTOR ANALYSIS

2004 ◽  
Vol 14 (01) ◽  
pp. 79-103 ◽  
Author(s):  
GILES AUCHMUTY
Keyword(s):  
Boundary Data ◽  
Vector Fields ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Orthogonal Decomposition ◽  
Vector Analysis ◽  
Mixed Case ◽  
Optimal Constants ◽  
Main Inequality

This paper proves some simple inequalities for Sobolev vector fields on nice bounded three-dimensional regions, subject to homogeneous mixed normal and tangential boundary data. The fields just have divergence and curl in L2. For the limit cases of prescribed zero normal, respectively zero tangential, data on the whole boundary, the inequalities were proved by Friedrichs who called the result the main inequality of vector analysis. For this mixed case, the optimal constants in the inequality are described, together with the fields for which equality holds. The detailed results depend on a special orthogonal decomposition and the analysis of associated eigenvalue problems.

Class of double-talk detectors based on the holder inequality

2011 ◽  
Author(s):  
Constantin Paleologu ◽  
Jacob Benesty ◽  
Tomas Gaensler ◽  
Silviu Ciochina
Keyword(s):  
Hölder Inequality

Behaviour of the Extended Hölder Inequality with Respect to the Index Set

1970 ◽  
Vol s2-2 (1) ◽  
pp. 121-124
Author(s):  
H. W. McLaughlin ◽  
F. T. Metcalf
Keyword(s):  
Hölder Inequality ◽  
Index Set
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