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Necessary condition for measures which are ( L q , L p ) multipliers

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2009)

Annales mathématiques Blaise Pascal

Let G be a locally compact group and ρ the left Haar measure on G . Given a non-negative Radon measure μ , we establish a necessary condition on the pairs q , p for which μ is a multiplier from L q G , ρ to L p G , ρ . Applied to n , our result is stronger than the necessary condition established by Oberlin in [14] and is closely related to a class of measures defined by Fofana in [7].When G is the circle group, we obtain a generalization of a condition stated by Oberlin [15] and improve on it in some cases.

New algebras of functions on topological groups arising from G-spaces

E. Glasner, M. Megrelishvili (2008)

Fundamenta Mathematicae

For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class...

Newtonian spaces: An extension of Sobolev spaces to metric measure spaces.

Nageswari Shanmugalingam (2000)

Revista Matemática Iberoamericana

This paper studies a possible definition of Sobolev spaces in abstract metric spaces, and answers in the affirmative the question whether this definition yields a Banach space. The paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored, and these various definitions are compared. The main tool used in this paper is the concept of moduli of path...

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