Ketaksamaan Operator Integral Fraksional yang Diperumum pada Ruang Morrey Tak Homogen yang Diperumum

Siti Rohmah Azizah, Hairur Rahman, Achmad Nasichuddin

Abstract


A Fractional integral operator is one of the operators in mathematical analysis. Fractional integral operator itself maps any real-valued function into the integral form  of the division of the at function. One of the expansion of fractional integral operator is generalized fractional integral operator. Morrey space is an extension of Lebesgue space. Morrey space is the set of all Lebesgue measurable functions, whose norm is finite over Morrey space. In this study, we will discuss the inequalities of the generalized fractional integral operator on a generalized non-homogeneous Morrey space. We proved of this inequality using the Chebyshev inequality and the Holder inequality.


Keywords


Fractional Integral Operators; Generalized Fractional Integral Operators; Generalized Non-homogeneous Morrey Space

Full Text:

PDF

References


Sawano, Y., Fazio, dan Hakim. Morrey Spaces: Introduction and Applications to Integral Operatos and PDE's Volume I. India: CRC Press. 2020.
Nakai, E. On generalized fractional integrals. Taiwanese J. Math. 5. 587-607. 2001.
Gunawan, H. A note on the generalized fractional integral operators. Bandung: Departement of Mathematics. ITB. 2003.
Hakim, Denny Ivanal, Hendra Gunawan. Weak (p,q) Inequalities for Fractional Integral Operators on Generalized Morrey Spaces of Non-Homogeneous type. Mathematica Acterna, vol. 3. No. 3. p. 161-168. 2013.
Li, Y., Gu, X., dan Zhao, J. The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hӧlder's Inequality. Symmetry, 10. 2018.
Eridani, H. Gunawan dan E. Nakai. On generalized fractional integral operators. Scientiac Mathematicae Japonicae Online, vol. 10. 307-318. 2004.
Sawano, Y. S. Sugano dan H. Tanaka. A Note on Generalized Fractional Integral Operators on Generalized Morrey Spaces. Hindawi Publishing Corporation. 1-18. 2009.
Garcia-Cuerva, J. dan A. Eduardo Gatto. Boundedness Properties of Fractional Integral Operators Associated to Non-Doubling Measures. Mathematics Subject Classification. 1-18. 2018.
Gunawan, H., Sihwaningrum, I. A weak-(p,q) Inequality for Fractional Integral Operator on Morrey spaces via Hedberg Type Inequality. JMP, vol.8. no.2. p. 103-108. 2016.




DOI: https://doi.org/10.18860/jrmm.v3i5.16970

Refbacks

  • There are currently no refbacks.