Mariusz Mirek

activity

20092026

most citedA bootstrapping approach to jump inequalities and their applications

29 citations · 181 across the 37 of their papers we have counts for

collaborators

Showing 2014 · math.CAShow all

3 papers · 2 filters

math.CA2014★ 22 cited

Variational estimates for averages and truncated singular integrals along the prime numbers

Mariusz Mirek, Bartosz Trojan, Pavel Zorin-Kranich

We prove, in a unified way, $r$ -variational estimates, $r > 2$ , on $ℓ^{s} (Z)$ spaces, $s \in (1, \infty)$ , for averages and truncated singular integrals along the set of…

math.CA2014★ 1 cited

Discrete maximal functions in higher dimensions and applications to ergodic theory

Mariusz Mirek, Bartosz Trojan

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational e…

math.CA2014★ 2 cited

$ℓ^{p} (Z)$ -- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems

Mariusz Mirek

We establish the first pointwise ergodic theorems along thin sets of prime numbers; a set with zero density with respect to the primes. For instance we will be able to achieve this…

Variational estimates for averages and truncated singular integrals along the prime numbers

Discrete maximal functions in higher dimensions and applications to ergodic theory

ℓp(Z) -- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems

$ℓ^{p} (Z)$ -- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems