Banach Journal of Mathematical Analysis

Sharp weighted bounds for fractional integrals via the two-weight theory

Vakhtang Kokilashvili, Alexander Meskhi, and Muhammad Asad Zaighum

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Abstract

We derive sharp weighted norm estimates for positive kernel operators on spaces of homogeneous type. Similar problems are studied for one-sided fractional integrals. Bounds of weighted norms are of mixed type. The problems are studied using the two-weight theory of positive kernel operators. As special cases, we derive sharp weighted estimates in terms of Muckenhoupt characteristics.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 3 (2018), 673-692.

Dates
Received: 9 October 2017
Accepted: 5 December 2017
First available in Project Euclid: 19 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1524124813

Digital Object Identifier
doi:10.1215/17358787-2017-0063

Mathematical Reviews number (MathSciNet)
MR3824746

Subjects
Primary: 31A10: Integral representations, integral operators, integral equations methods 42B25: Maximal functions, Littlewood-Paley theory 30C40: Kernel functions and applications

Keywords
integral operators with positive kernels potentials fractional maximal functions spaces of homogeneous type one-sided fractional integrals

Citation

Kokilashvili, Vakhtang; Meskhi, Alexander; Zaighum, Muhammad Asad. Sharp weighted bounds for fractional integrals via the two-weight theory. Banach J. Math. Anal. 12 (2018), no. 3, 673--692. doi:10.1215/17358787-2017-0063. https://projecteuclid.org/euclid.bjma/1524124813


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