An induction principle for spectral and rearrangement inequalitities
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- by Kong Ming Chong PDF
- Trans. Amer. Math. Soc. 196 (1974), 371-383 Request permission
Abstract:
In this paper, expressions of the form $f \prec g$ or $f \prec \prec g$ (where $\prec$ and $\prec \prec$ denote the Hardy-Littlewood-Pólya spectral order relations) are called spectral inequalities. Here a general induction principle for spectral and rearrangement inequalities involving a pair of n-tuples in ${R^n}$ as well as their decreasing and increasing rearrangements is developed. This induction principle proves that such spectral or rearrangement inequalities hold iff they hold for the case when $n = 2$, and that, under some mild conditions, this discrete result can be generalized to include measurable functions with integrable positive parts. A similar induction principle for spectral and rearrangement inequalities involving more than two measurable functions is also established. With this induction principle, some well-known spectral or rearrangement inequalities are obtained as particular cases and additional new results given.References
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K. M. Chong, Equimeasurable rearrangements of functions with applications to analysis, Thesis, Queen’s University, Kingston, Ontario, Canada, 1972.
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 196 (1974), 371-383
- MSC: Primary 26A87
- DOI: https://doi.org/10.1090/S0002-9947-1974-0344396-7
- MathSciNet review: 0344396