Subadditive inequalities for operators

Submajorization inequalities associated with $tau$-measurable operators

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

On Inequalities for Differential Operators

In this paper we study the following problem: Given that certain functionals of u and its derivatives belong to given Lclasses over the infinite interval, what can be said about the L-classes of other functionals? Utilizing a simple device from the theory of linear differential equations, we obtain a number of results due to Landau, Kolmogoroff, Halperin-von Neumann, and Nagy, together with som...

From Subadditive Inequalities of Singular Values to Triangle Inequalities of Canonical Angles

Lφ Integral Inequalities for Maximal Operators

Sufficient (almost necessary) conditions are given on the weight functions u(·), v(·) for Φ−1 2 [ ∫ Rn Φ2 ( C2(Msf)(x) ) u(x)dx ] ≤ Φ−1 1 [ C1 ∫ Rn Φ1(|f(x)|)v(x)dx ] to hold when Φ1, Φ2 are φ-functions with subadditive Φ1Φ 2 , and Ms (0 ≤ s < n), is the usual fractional maximal operator. §

Weighted Norm Inequalities for Fractional Operators

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels. Indiana Univ. Ma...