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Matrix-weighted fractional type operators on spaces of homogeneous type

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Published/Copyright: March 28, 2025
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Abstract

In this paper, we introduce matrix A p , q weights on spaces of homogeneous type in the sense of Coifman and Weiss, and prove some basic properties of these weights. As applications, the necessary and sufficient condition for the boundedness of matrix-weighted fractional maximal operators on Lebesgue spaces is established, and the boundedness of matrix-weighted fractional integral operators on Lebesgue spaces is obtained.

Award Identifier / Grant number: 12061069

Funding statement: The research was supported by National Natural Science Foundation of China (Grant No. 12061069).

Acknowledgements

The authors thank the referees for their careful reading and helpful comments which indeed improved the presentation of this article.

References

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Received: 2024-05-13
Revised: 2024-11-05
Accepted: 2024-11-08
Published Online: 2025-03-28
Published in Print: 2025-10-01

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