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arXiv · 2603.29564

Estimates for tail functions under Riesz transforms in Grand Lebesgue Spaces

Maria Rosaria Formica·Eugene Ostrovsky·Leonid Sirota
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Abstract

We study the tail behaviour of measurable functions under generalized Riesz-type operators in the framework of Grand Lebesgue Spaces. By exploiting the connection between the growth of $L^p$ norms and the Young--Fenchel transform, we derive explicit tail estimates from suitable $L^p$ bounds. We also present model examples and apply the abstract result to the classical Riesz transforms, showing how the $L^p$ growth of the operator interacts with the intrinsic tail behaviour of the input function.

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Maria Rosaria Formica, Eugene Ostrovsky, Leonid Sirota. 2026-03-31. Estimates for tail functions under Riesz transforms in Grand Lebesgue Spaces. https://arxiv.org/abs/2603.29564

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