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].
Dedicated to Professor V. Kokilashvili on the occasion of his 80th birthday
Funding source: Japan Society for the Promotion of Science
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.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture