On the behavior of integrable functions at infinity

Andrzej Komisarski

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arXiv · 1601.01241

On the behavior of integrable functions at infinity

Andrzej Komisarski

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Abstract

We investigate the behavior of sequences $(f(c_nx))$ for Lebesgue integrable functions $f:\mathbb R^d\to\mathbb R$. In particular, we give a~description of classes of multipliers $(c_n)$ and $(d_n)$ such that $f(c_nx)\to0$ or $\sum_{n=1}^\infty|f(d_nx)|<\infty$ for $λ$ almost every $x\in\mathbb R^d$.

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BibTeX RIS

Andrzej Komisarski. 2016-01-06. On the behavior of integrable functions at infinity. https://arxiv.org/abs/1601.01241

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