Banach Journal of Mathematical Analysis

Square function inequalities for monotone bases in L1

Adam Osękowski

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We describe a novel method of handling general sharp square function inequalities for monotone bases and contractive projections in L1. The technique rests on the construction of an appropriate special function enjoying certain size and convexity-type properties. As an illustration, we establish a strong L1L1 and a weak-type L1L1, estimate for square functions.

Article information

Banach J. Math. Anal., Volume 12, Number 3 (2018), 693-708.

Received: 3 December 2017
Accepted: 28 February 2018
First available in Project Euclid: 16 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B15: Summability and bases [See also 46A35]
Secondary: 46A35: Summability and bases [See also 46B15] 46B20: Geometry and structure of normed linear spaces

contractive projection Haar system square function monotone basis


Osękowski, Adam. Square function inequalities for monotone bases in $L^{1}$. Banach J. Math. Anal. 12 (2018), no. 3, 693--708. doi:10.1215/17358787-2018-0004.

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