Abstract
We introduce conditions on the construction of grand Lebesgue spaces on ℝn which imply the validity of the Sobolev theorem for the Riesz fractional integrals Iα and the boundedness of the maximal operator, in such spaces. We also give an inversion of the operator Iα by means of hypersingular integrals, within the frameworks of the introduced spaces. We also proof the denseness of
Acknowledgements
This research was supported by Russian Fund of Basic Research, the grant 15-01-02732 in the case of the first author and the grant 15-31-50241 in the case of the second author.
References
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© 2016 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA-volume 19-3-2016)
- Survey Paper
- Fractional integrals and derivatives: mapping properties
- Research Paper
- Riesz fractional integrals in grand lebesgue spaces on ℝn
- Survey Paper
- United lattice fractional integro-differentiation
- Research Paper
- Integral equations of fractional order in Lebesgue spaces
- Research Paper
- General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
- Research Paper
- Multilinear integral operators in weighted grand Lebesgue spaces
- Research Paper
- Fractional integration operator on some radial rays and intertwining for the Dunkl operator
- Research Paper
- Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
- Research Paper
- Existence and uniqueness of global solutions of caputo-type fractional differential equations
- Research Paper
- Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA-volume 19-3-2016)
- Survey Paper
- Fractional integrals and derivatives: mapping properties
- Research Paper
- Riesz fractional integrals in grand lebesgue spaces on ℝn
- Survey Paper
- United lattice fractional integro-differentiation
- Research Paper
- Integral equations of fractional order in Lebesgue spaces
- Research Paper
- General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
- Research Paper
- Multilinear integral operators in weighted grand Lebesgue spaces
- Research Paper
- Fractional integration operator on some radial rays and intertwining for the Dunkl operator
- Research Paper
- Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
- Research Paper
- Existence and uniqueness of global solutions of caputo-type fractional differential equations
- Research Paper
- Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems