Supremal Generators of Spaces of Homogeneous Functions1

Banach Spaces and Algebras of Continuous Functions1

From 1-homogeneous Supremal Functionals to Difference Quotients: Relaxation and Γ-convergence

In this paper we consider positively 1-homogeneous supremal functionals of the type F (u) := supΩ f(x,∇u(x)). We prove that the relaxation F̄ is a difference quotient, that is F̄ (u) = RF (u) := sup x,y∈Ω, x6=y u(x)− u(y) dF (x, y) for every u ∈ W (Ω), where dF is a geodesic distance associated to F . Moreover we prove that the closure of the class of 1-homogeneous supremal functionals with respe...

Hereditarily Homogeneous Generalized Topological Spaces

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

IteratedHardy-type inequalities involving suprema

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...