Bartosz Trojan

Discrete maximal functions in higher dimensions and applications to ergodic theory

We establish a higher dimensional counterpart of Bourgains pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates

Cotlar’s Ergodic Theorem Along the Prime Numbers

V_r

VARIATIONAL ESTIMATES FOR AVERAGES AND TRUNCATED SINGULAR INTEGRALS ALONG THE PRIME NUMBERS

on

L^p(Z^d)-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates

L^p

ASYMPTOTIC BEHAVIOR OF DENSITIES OF UNIMODAL CONVOLUTION SEMIGROUPS

spaces for all

\ell ^p\left( \mathbb {Z}^d\right) -estimates for discrete operators of Radon type: variational estimates

1<p<\infty

\ell^p(\mathbb Z^d)-estimates for discrete operators of Radon type: variational estimates

and

L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

r>\max\{p, p/(p-1)\}

Hua System and Pluriharmonicity for Symmetric Irreducible Siegel Domains of Type II

. Moreover, we obtain the estimates which are uniform in the coefficients of a polynomial mapping of fixed degree.

Limit theorems for random walks

The aim of this paper is to prove Cotlar’s ergodic theorem modeled on the set of primes.