The $(L^{p},L^{1})$ bilinear Hardy-Littlewood function and Furstenberg averages
I.Assani, Z. Buczolich
TL;DR
This paper investigates the $(L^{p},L^{1})$ bilinear Hardy-Littlewood function and Furstenberg averages, focusing on the tail behavior rather than the averages themselves, with a prior verified version addressing the tail analysis.
Contribution
The paper provides a complete and correct analysis of the tail behavior of the bilinear Hardy-Littlewood function and Furstenberg averages, excluding the average analysis.
Findings
Tail analysis of the bilinear Hardy-Littlewood function completed
Previous version verified as complete and correct
Focus shifted away from averages to tail behavior
Abstract
More work needs to be done to move from the tail to the averages themselves. So at this time we prefer to withdraw the paper about the averages. However a previous version of the paper which deals with the tail has been checked and we believe it to be complete and correct.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Mathematical Approximation and Integration