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Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces

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Published/Copyright: April 17, 2018
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Abstract

In this paper, we aim to deal with the boundedness and the weak-type boundedness for the generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 2017, 2, 159–190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 2017, 7, 534–546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

MSC 2010: 26A33; 42B25; 42B35

Dedicated to Professor V. Kokilashvili on the occasion of his 80th birthday


Award Identifier / Grant number: 15K04929

Award Identifier / Grant number: 15K04929

Funding statement: The first author was partially supported by Grant-in-Aid for Scientific Research (C), no. 16K05209, Japan Society for the Promotion of Science. The second author was partially supported by Grant-in-Aid for Scientific Research (C), no. 15K04929, Japan Society for the Promotion of Science.

Acknowledgements

The authors are thankful to Dr. Denny Ivanal Hakim for him pointing out the paper [2] to connect our fractional integral operator to the actual application to PDE.

References

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Received: 2017-7-10
Revised: 2018-1-29
Accepted: 2018-2-1
Published Online: 2018-4-17
Published in Print: 2018-6-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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