Nonlinear Inequalities with Double Riesz Potentials

Reverse Triangle Inequalities for Riesz Potentials and Connections with Polarization

We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main tool used in the proofs is the representation for a power of the farthest distance function as a Riesz potential of a unit Borel measure. MSC 2010. P...

The Stein–weiss Type Inequalities for the B–riesz Potentials

We establish two inequalities of Stein-Weiss type for the Riesz potential operator Iα,γ (B−Riesz potential operator) generated by the Laplace-Bessel differential operator ΔB in the weighted Lebesgue spaces Lp,|x|β ,γ . We obtain necessary and sufficient conditions on the parameters for the boundedness of Iα,γ from the spaces Lp,|x|β ,γ to Lq,|x|−λ ,γ , and from the spaces L1,|x|β ,γ to the weak...

Riesz Transform and Riesz Potentials for Dunkl Transform

Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.

Deviations of Riesz Projections of Hill Operators with Singular Potentials

On Continuity of Generalized Riesz Potentials

This study establishes the theorem on continuity of generalized Riesz potentials with non-isotropic kernels depending on (β, γ)-distance. Mathematics Subject Classification: 31B10, 42B20, 47B06