Abstract
We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including Lp-Lq, Lp-BMO and Lp-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.
Acknowledgements
This work was supported by CONICET, ANPCyT and CAI+D (UNL).
References
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© 2018 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 21–3–2018)
- Research Paper
- Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
- Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance
- The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces
- Parallel algorithms for modelling two-dimensional non-equilibrium salt transfer processes on the base of fractional derivative model
- Some iterated fractional q-integrals and their applications
- Lebesgue regularity for nonlocal time-discrete equations with delays
- Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions
- Error estimates of high-order numerical methods for solving time fractional partial differential equations
- The Laplace transform induced by the deformed exponential function of two variables
- Attractivity for fractional evolution equations with almost sectorial operators
- The multiplicity solutions for nonlinear fractional differential equations of Riemann-Liouville type
- Well-posedness of general Caputo-type fractional differential equations
- Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions
- Inverse source problem for a space-time fractional diffusion equation
- Erratum
- Erratum to: Invariant subspace method: A tool for solving fractional partial differential equations, in: FCAA-20-2-2017
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 21–3–2018)
- Research Paper
- Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
- Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance
- The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces
- Parallel algorithms for modelling two-dimensional non-equilibrium salt transfer processes on the base of fractional derivative model
- Some iterated fractional q-integrals and their applications
- Lebesgue regularity for nonlocal time-discrete equations with delays
- Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions
- Error estimates of high-order numerical methods for solving time fractional partial differential equations
- The Laplace transform induced by the deformed exponential function of two variables
- Attractivity for fractional evolution equations with almost sectorial operators
- The multiplicity solutions for nonlinear fractional differential equations of Riemann-Liouville type
- Well-posedness of general Caputo-type fractional differential equations
- Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions
- Inverse source problem for a space-time fractional diffusion equation
- Erratum
- Erratum to: Invariant subspace method: A tool for solving fractional partial differential equations, in: FCAA-20-2-2017