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Some conjectures about integral means of ∂f and ∂¯f
(2011)
We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the ...
Inequalities of correlation type for symmetric stable random vectors
(2011)
We point out a certain class of functions f and g for which random variables f(X1,...,Xm) and g(Xm+1,...,Xk) are non-negatively correlated for any symmetric jointly stable random variables Xi. We also show another result ...
Comparison of sums of independent identically distributed random variables
(2011)
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ∥Sk∥ with that of ∥Sj∥, and deduce some tail distribution maximal ...
Orlicz-Lorentz Spaces
(2011)
The purpose of this article is to summerize some recent results of the author about Orlicz-Lorentz spaces - function spaces that provide a common generalization of Orlicz spaces and Lorentz spaces.
Decomposition of analytic measures on groups and measure spaces
(2011)
This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of ...
The annular hull theorems for the kinematic dynamo operator for an ideally conducting fluid
(2011)
The group generated by the kinematic dynamo operator in the space of continuous divergence-free sections of the tangent bundle of a smooth manifold is studied. As shown in previous work, if the underlying Eulerian flow is ...
The Distribution of Non-Commutative Rademacher Series
(2011)
We give a formula for the tail of the distribution of the non-commutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm ...
p-summing operators on injective tensor products of spaces
(2011)
Let X, Y and Z be Banach spaces, and let Πp(Y,Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T:X⊗εY→Z is 1-summing if and only if a ...
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
(2011)
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to ...
Conditions implying regularity of the three dimensional Navier-Stokes equation
(2011)
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac ...
Complemented subspaces of spaces obtained by interpolation
(2011)
If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0,A1) such that A0 and A1 are isometric to X⊕V, and any intermediate space obtained using ...
The Hardy operator and Boyd indices
(2011)
We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.
The spectrum of the kinematic dynamo operator for an ideally conducting fluid
(2011)
The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in
the space of continuous divergence free vector fields on a compact Riemannian manifold ...
Contraction and decoupling inequalities for multilinear forms and u-statistics
(2011)
We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz ...
Finite time blow up for a Navier-Stokes like equation
(2011)
We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a ...
Lyapunov theorems for Banach spaces
(2011)
We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for E-valued functions. This characterization ...
Hahn's embedding theorem for orders and harmonic analysis on groups with ordered duals
(2011)
Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on Lp(G), 1 ≤ p < ∞, as was done by Helson. We will show how to ...
Evolutionary semigroups and Lyapunov theorems in Banach spaces
(2011)
We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from ...
Temperature and heat flux estimation from sampled transient sensor measurements
(2011)
Laplace transform is used to solve the problem of heat conduction over a finite slab. The temperature and heat flux on the two surfaces of a slab are related by the transfer functions. These relationships can be used to ...
Decoupling inequalities for the tail probabilities of multivariate u-statistics
(2011)
In this paper we present a decoupling inequality that shows that multivariate U-statistics can be studied as sums of (conditionally) independent random variables. This result has important implications in several areas of ...