2022 On the Extension of the Reverse Hölder Inequality for Power Functions on the Real Axis
Alina A. Shalukhina
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Real Anal. Exchange 47(2): 425-434 (2022). DOI: 10.14321/realanalexch.47.2.1653382423


We consider the class of all nonnegative on $\mathbb R_+$ functions such that each of them satisfies the reverse Hölder inequality uniformly over all intervals with some constant, the minimum value of which can be regarded as the corresponding “norm” of a function. We compare this “norm” with the “norm” of the even extension of a function from $\mathbb R_+$ on $\mathbb R$. In this paper, an upper estimate for the ratio of such “norms” has been obtained. For the special case of power functions on $\mathbb R_+$, we give the precise value of the “norm” increase caused by even extension. This value is a lower estimate for the analogous quantity in the case of arbitrary functions. It has been shown that the obtained upper and lower estimates for the general case are asymptotically sharp.


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Alina A. Shalukhina. "On the Extension of the Reverse Hölder Inequality for Power Functions on the Real Axis." Real Anal. Exchange 47 (2) 425 - 434, 2022. https://doi.org/10.14321/realanalexch.47.2.1653382423


Published: 2022
First available in Project Euclid: 10 February 2023

Digital Object Identifier: 10.14321/realanalexch.47.2.1653382423

Primary: 26D10
Secondary: 42B25

Keywords: even extension , power function , reverse Hölder inequality

Rights: Copyright © 2022 Michigan State University Press


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Vol.47 • No. 2 • 2022
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