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Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions — Corrigendum

Published online by Cambridge University Press:  04 June 2021

Amiran Gogatishvili
Affiliation:
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Z̆ıtna 25, 11567 Praha 1, Czech Re-public ([email protected])
Júlio S. Neves
Affiliation:
University of Coimbra, CMUC, Department of Mathematics, Apartado 3008, EC Santa Cruz, 3001-454Coimbra, Portugal ([email protected])
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Abstract

Type
Corrigendum
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

We correct some misprints in some powers that propagate throughout the paper with title “Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions”, Proceedings of the Royal Society of Edinburgh, 150, 17–39, 2020 DOI:10.1017/prm.2018.85

Where is $x^{\lambda p(1-p)}$ should be $x^{(\lambda pp^{\prime}-1)(1-p)}$ in:

p. 24 Theorem 3.1, eq. (3.2);

p. 24 line -6;

p. 26 line 1.

Where is $x^{\lambda {{p \over s}}\left( {1-{{p \over s}}} \right)}$ should be $x^{\left( {\lambda {{p \over s}}{\left( {{p \over s}} \right)}^{\prime}-1} \right)\left( {1-{{p \over s}}} \right)}$ in:

p. 26 Theorem 3.2 - eq. (3.5).

Where is yλp should be y λp−1 in:

p. 33 → B 8, B 9, B 10, B 11;

p. 34 → B 12, B 13, B 14, B 15.

Where is xλp should be x λp−1 in:

p. 34 → B 15, B 16, B 17.

Where is z λp should be z −λp−1 in: p. 34 → B 18;

p. 35 → B 22, B 23, B 24, B 25.

Where is $V_{\lambda p}^{1-{p}^{\prime}} $ should be $V_{\lambda p}^{-1-{p}^{\prime}} $ in:

p. 33 → B 8, B 9, B 10, B 11;

p. 34 → B 12, B 13, B 14, B 15 (2 times), B 16, B 17, B 18;

p. 35 → B 22, B 23, B 24, B 25.

Acknowledgements

This research was partially supported by the grant 18-00580S of the Grant Agency of the Czech Republic, RVO: 67985840 and by CMUC (the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2020), funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.