## Banach Journal of Mathematical Analysis

### Square function inequalities for monotone bases in $L^{1}$

#### Abstract

We describe a novel method of handling general sharp square function inequalities for monotone bases and contractive projections in $L^{1}$. 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 $L^{1}\to L^{1}$ and a weak-type $L^{1}\to L^{1,\infty}$ estimate for square functions.

#### Article information

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

Dates
Accepted: 28 February 2018
First available in Project Euclid: 16 June 2018

https://projecteuclid.org/euclid.bjma/1529114493

Digital Object Identifier
doi:10.1215/17358787-2018-0004

Mathematical Reviews number (MathSciNet)
MR3824747

Zentralblatt MATH identifier
06946077

#### Citation

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. https://projecteuclid.org/euclid.bjma/1529114493

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