Maximal Inequalities in Bilateral Grand Lebesque Spaces Over Unbounded Measure

Abstract

In this paper non-asymptotic exact rearrangement invariant norm estimates are derived for the maximum distribution of the family elements of some rearrangement invariant (r.i.) space over unbounded measure in the entropy terms and in the terms of generic chaining. We consider some applications in the martingale theory and in the theory of Fourier series.

Ostrovsky E., Rogover E

References in corpus (3)

• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
• Exponential Orlicz Spaces: New Norms and Applications
• Exponential Bounds in the Law of Iterated Logarithm for Martingales