Abstract
We invent a class of infinite matrices \( A =(a_{j,k})^{\infty}_{j,k=0}\) called (p,q)-maximizing; its definition (see Definition 1 in Sect. 2.1.3) is motivated by a number of classical maximal inequalities intimately related with almost sure summation of orthogonal series with respect to Cesàro, Riesz, and Abel summation.
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© 2011 Springer-Verlag Berlin Heidelberg
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Defant, A. (2011). Commutative Theory. In: Classical Summation in Commutative and Noncommutative L<sub>p</sub>-Spaces. Lecture Notes in Mathematics(), vol 2021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20438-8_2
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DOI: https://doi.org/10.1007/978-3-642-20438-8_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20437-1
Online ISBN: 978-3-642-20438-8
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