Generalized Bessel and Riesz Potentials on Metric Measure Spaces

Multipliers of generalized frames in Hilbert spaces

Hilbert spaces

• Pre-Hilbert spaces: definition • Cauchy-Schwarz-Bunyakowski inequality • Example: spaces ` • Triangle inequality, associated metric, continuity issues • Hilbert spaces, completions, infinite sums • Minimum principle • Orthogonal projections to closed subspaces • Orthogonal complements W⊥ • Riesz-Fischer theorem on linear functionals • Orthonormal sets, separability • Parseval equality, Bessel...

G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

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...

Common fixed point results on vector metric spaces

In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize well-known comparable results in the literature.