New Results for the Hardy Integral Inequality Based on the Change of Variables Point of View
Year: 2025
Type: article
Abstract: The Hardy integral inequality is a key result in analysis and plays an important role in many areas of mathematics. It has been proved in various ways, including a direct one combining a change of variables and the Minkowski integral inequality. However, the approach of using change of variables perspectives to deepen the understanding of the Hardy integral inequality and to extend its scope seems to be underexplored. This paper fills this gap in two complementary ways. First, using change of variables techniques, we show that the ”optimal” constant factor of the Hardy integral inequality can be significantly improved under basic assumptions on the main function. Second, using similar techniques, we generalize the Hardy integral inequality using three intermediate functions. A new adaptable integral inequality is thus introduced. Several examples are given to support the theoretical results.
Source: Selcuk Journal of Science
DOI: 10.63673/sjs.1720054
Author: Christophe Chesneau
Institution: Université de Caen Normandie
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4416848156
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