Fubini theorem and generalized Minkowski inequality for the pseudo-integral

2020 ◽  
Vol 122 ◽  
pp. 9-23 ◽  
Author(s):  
Deli Zhang ◽  
Endre Pap
Keyword(s):  
Minkowski Inequality ◽  
Fubini Theorem

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.

scholarly journals A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral

2011 ◽  
Vol 9 (3) ◽  
pp. 283-304 ◽  
Author(s):  
A. Boccuto ◽  
D. Candeloro ◽  
A. R. Sambucini
Keyword(s):  
Type Theorem ◽  
Riesz Space ◽  
Fubini Theorem ◽  
Real Plane ◽  
Henstock Integral ◽  
Riesz Spaces

A Fubini-type theorem is proved, for the Kurzweil-Henstock integral of Riesz-space-valued functions defined on (not necessarily bounded) subrectangles of the “extended” real plane.

The Fubini Theorem

1978 ◽  
pp. 91-105
Author(s):  
Jan Mikusiński
Keyword(s):  
Fubini Theorem

Prescribing Centro-Affine Curvature From One Convex Body to Another

2020 ◽  
Author(s):  
Alina Stancu
Keyword(s):  
Convex Body ◽  
Convex Bodies ◽  
Minkowski Inequality ◽  
Curvature Flow ◽  
Constant Volume ◽  
Convex Hypersurface ◽  
Strictly Convex ◽  
Initial Hypersurface ◽  
Affine Curvature ◽  
Convex Hypersurfaces

Abstract We study a curvature flow on smooth, closed, strictly convex hypersurfaces in $\mathbb{R}^n$, which commutes with the action of $SL(n)$. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in $\mathbb{R}^n$ with centro-affine curvature proportional, but not always equal, to the centro-affine curvature of a fixed hypersurface. We outline some consequences of this result for the geometry of convex bodies and the logarithmic Minkowski inequality.

On the Case of Equality in the Brunn-Minkowski Inequality for Capacity

Inequalities ◽  
2002 ◽  
pp. 497-511
Author(s):  
Luis A. Caffarelli ◽  
David Jerison ◽  
Elliott H. Lieb
Keyword(s):  
Minkowski Inequality

scholarly journals A Fubini theorem for iterated stochastic integrals

1978 ◽  
Vol 84 (1) ◽  
pp. 159-161 ◽  
Author(s):  
Marc A. Berger ◽  
Victor J. Mizel
Keyword(s):  
Fubini Theorem ◽  
Stochastic Integrals

Orlicz Addition for Measures and an Optimization Problem for the -divergence

2019 ◽  
Vol 72 (2) ◽  
pp. 455-479
Author(s):  
Shaoxiong Hou ◽  
Deping Ye
Keyword(s):  
Optimization Problem ◽  
Jensen’S Inequality ◽  
Minkowski Inequality ◽  
Isoperimetric Inequalities ◽  
Jensen's Inequality ◽  
Dual Functional ◽  
Two Measures ◽  
Star Bodies

AbstractThis paper provides a functional analogue of the recently initiated dual Orlicz–Brunn–Minkowski theory for star bodies. We first propose the Orlicz addition of measures, and establish the dual functional Orlicz–Brunn–Minkowski inequality. Based on a family of linear Orlicz additions of two measures, we provide an interpretation for the famous $f$-divergence. Jensen’s inequality for integrals is also proved to be equivalent to the newly established dual functional Orlicz–Brunn–Minkowski inequality. An optimization problem for the $f$-divergence is proposed, and related functional affine isoperimetric inequalities are established.

An Unsymmetric Fubini Theorem

1984 ◽  
Vol 91 (2) ◽  
pp. 131-133 ◽  
Author(s):  
G. W. Johnson
Keyword(s):  
Fubini Theorem
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