Abstract
This paper is a follow up of a recent work of the author and Y. Sawano [6], in 2019. We investigate the boundedness of the bilinear fractional integral operator introduced by Grafakos in [3], 1992. When the local integrability index s falls 1 with weights and t exceeds 1, He and Yan obtained some results on this operator was worked on Morrey spaces earlier in [7] 2018. Later in the paper [6] we considered the case t = 1. This paper handles the remaining case 0 < t < 1.
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Acknowledgements
The author would like to be thankful to his advisor Professor Kotaro Tsugawa for his guidance and advise, and be grateful to Professor Yoshihiro Sawano, in Tokyo Metropolitan University, for his many kinds of ideas and answering many questions. In particular, Sawano gave him a hint to Theorem 2.2.
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Hatano, N. Bilinear estimates on Morrey spaces by using average. Anal Math 46, 283–291 (2020). https://doi.org/10.1007/s10476-020-0031-0
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DOI: https://doi.org/10.1007/s10476-020-0031-0