2022/04/05 by G. J. O. Jameson
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Advanced Banach Space Theory
paper · pdf · doi:10.1080/00029890.2022.2051407
A classical inequality of G. H. Hardy states that Cx≤2x for x in l2, where C is the Cesàro (alias averaging) operator. This inequality has been strengthened to (C−I)x≤x. It has also been shown that CTx≤Cx for x in l2. We present equalities that imply these inequalities, together with the reverse inequalities (C−I)x≥(1/√2)x and Cx≤√2CTx. We also present companion results involving the shift operator.