Vector-valued maximal inequalities and multiparameter oscillation inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Ergodic theorems, spectral theory, Markov operators (37A30) Relations between ergodic theory and number theory (37A44) Relations between ergodic theory and harmonic analysis (37A46)

Cites Work

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Variation estimates for averages along primes and polynomials
Proof of the ergodic theorem.
Estimates for the square variation of partial sums of Fourier series and their rearrangements
Cotlar's ergodic theorem along the prime numbers
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Maximal and singular integral operators via Fourier transform estimates
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Discrete analogues in harmonic analysis: spherical averages
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Discrete maximal functions in higher dimensions and applications to ergodic theory
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Strong variational and jump inequalities in harmonic analysis
Oscillation in ergodic theory
Proof of the Quasi-Ergodic Hypothesis
ERGODIC THEORY AND TRANSLATION-INVARIANT OPERATORS
THE IONESCU–WAINGER MULTIPLIER THEOREM AND THE ADELES
Some remarks on oscillation inequalities
Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes

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