Terry R. McConnell

On Fourier multiplier transformations of Banach-valued functions

We obtain analogues of the Mihlin multiplier theorem and Littlewood-Paley inequalities for functions with values in a suitable Banach space B. The requirement on B is that it have the unconditionality property for martingale difference sequences.

Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables

SummaryLet E be a Banach space and Π: E→ℝ+ be symmetric, continuous and convex. Let {Ui} and {ri} be independent sequences of random variables having, respectively, U(0, 1) and symmetric Bernoulli distributions, and let {Ui(j)} and {ri(j)} for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities

Two-parameter strong laws and maximal inequalities for U-statistics

E\Phi (\sum\limits_{\underset{\raise0.3em\hbox{

Exit times of N-dimensional random walks

\smash{\scriptscriptstyle-}

A conformal inequality related to the conditional gauge theorem

}}{i} \in \mathbb{Z}_ + ^d } {r_{i_1 } } ...r_{i_d } F_{\underset{\raise0.3em\hbox{

Stable-bounded subsets of Lα, and sample unboundedness of symmetric stable processes

\smash{\scriptscriptstyle-}

The lifetime of conditioned Brownian motion

}}{i} } (U_{i_1 } ,...,U_{i_d } ))

On the Position of a Random Walk at the Time of First Exit from a Sphere

and their “decoupled” versions