| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
Variable exponent Lebesgue spaces and Sobolev spaces have been intensively investigated for the past twenty years to discuss nonlinear partial differential equations with non-standard growth condition. These spaces have attracted more and more attention in connection with the study of elasticity and electrorheological fluids. In this research, we studied the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz-Morrey spaces and Musielak-Orlicz spaces. As an application of the boundedness of the maximal operator, we established a generalization of Sobolev's inequality for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces and Musielak-Orlicz spaces. We also established generalizations of Sobolev's inequality for double phase functionals.
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