Shifts of a Measurable Function and Criterion of p-integrability

Boris Mityagin

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arXiv · 1608.07860

Shifts of a Measurable Function and Criterion of p-integrability

Boris Mityagin

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Abstract

It is shown that two conditions $f(a + \cdot) - f(\cdot) \in L^p(R)$, and $(\sin b \cdot) f(\cdot) \in L^p(R)$ guarantee $f \in L^p(R)$, $1 \leq p < \infty$, if and only if $ab$ is not in $(\pi Z)$.

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Boris Mityagin. 2016-08-28. Shifts of a Measurable Function and Criterion of p-integrability. https://arxiv.org/abs/1608.07860

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