Scholarlink

<p>The establishment of new integral inequalities is important in several areas of mathematics, including the analysis of functional spaces and study of partial differential equations. In this paper, we contribute to the subject by proving a new general type of Hilbert integral inequality whose main double integral has the property of depending on an adaptive trivariate function. The proof makes use of a “quadratic polar change-of-variables technique”, which is advantageous for its tractability and elegance. Furthermore, it is an underexplored technique in this context, so our developments may inspire research in this direction. Several examples are given, including old and new integral inequalities.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A new type of general Hilbert integral inequality with examples

  • 期刊论文

  • 发表日期：

    2025年4月5日

查看全文
  • Christophe Chesneau

摘要

The establishment of new integral inequalities is important in several areas of mathematics, including the analysis of functional spaces and study of partial differential equations. In this paper, we contribute to the subject by proving a new general type of Hilbert integral inequality whose main double integral has the property of depending on an adaptive trivariate function. The proof makes use of a “quadratic polar change-of-variables technique”, which is advantageous for its tractability and elegance. Furthermore, it is an underexplored technique in this context, so our developments may inspire research in this direction. Several examples are given, including old and new integral inequalities.