Abstract
The boundedness of multi(sub)linear Hardy–Littlewood maximal, Calderón–Zygmund and fractional integral operators defined on metric measure spaces is established in weighted grand Lebesgue spaces. In particular, we derive the one-weight inequality for maximal and singular integrals under the Muckenhoupt type conditions, weighted Sobolev type theorem and trace type inequality for fractional integrals.
Dedicated to Professor Stefan G. Samko on the occasion of his 75th anniversary
Acknowledgements
The first and third named authors were partially supported by the Shota Rustaveli National Science Foundation Grant (Contract Numbers: D/13–23 and 31/47). The second named author was supported by National Science Centre, Poland, project no. 2015/17/B/ST1/00064.
The authors are thankful to Prof. V. Kiryakova for remarks and suggestions which made the manuscript better than the initial version.
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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
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- United lattice fractional integro-differentiation
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- Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
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- Existence and uniqueness of global solutions of caputo-type fractional differential equations
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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