Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 1 (2019), 26-46.
Continuous generalization of Clarkson–McCarthy inequalities
Let be a compact Abelian group, let be the corresponding Haar measure, and let be the Pontryagin dual of . Furthermore, let denote the Schatten class of operators on some separable infinite-dimensional Hilbert space, and let denote the corresponding Bochner space. If is the mapping belonging to , then If is a finite group, then the previous equations comprise several generalizations of Clarkson–McCarthy inequalities obtained earlier (e.g., or ), as well as the original inequalities, for . We also obtain other related inequalities.
Banach J. Math. Anal., Volume 13, Number 1 (2019), 26-46.
Received: 17 January 2018
Accepted: 19 April 2018
First available in Project Euclid: 28 September 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47A30: Norms (inequalities, more than one norm, etc.)
Secondary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Kečkić, Dragoljub J. Continuous generalization of Clarkson–McCarthy inequalities. Banach J. Math. Anal. 13 (2019), no. 1, 26--46. doi:10.1215/17358787-2018-0014. https://projecteuclid.org/euclid.bjma/1538121808