. C A ] 1 6 Ju n 20 09 When is a Riesz distribution a complex measure ?

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

2 9 Ju n 20 09 Adams inequalities on measure spaces

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams’ results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels sati...

The Sharp Riesz Potential Estimates in Metric Spaces

We introduce the Riesz potential operator for functions deened on a quasi-metric space endowed with a nonnegative doubling measure satisfying certain lower bound for the measure of a ball. For this operator we prove sharp Lorentz-norm estimates in the spirit of the results due to O'Neil and Peetre (in the non-limiting case) and to Hansson and Brrzis{Wainger (in the limiting case). One of the fo...

A New Approach to Continuous Riesz Bases

This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

ar X iv : 0 90 6 . 48 35 v 1 [ m at h . O C ] 2 6 Ju n 20 09 The Complex Gradient Operator and the CR - Calculus