Remark on the inequality of F. Riesz
Volume 68 / 2005
Banach Center Publications 68 (2005), 95-97
MSC: Primary 42C05; Secondary 30B62.
DOI: 10.4064/bc68-0-11
Abstract
We prove F. Riesz' inequality assuming the boundedness of the norm of the first arithmetic mean of the functions $\left| \varphi _{n}\right| ^{p}$ with $p\geq 2$ instead of boundedness of the functions $\varphi _{n}$ of an orthonormal system.
