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A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra ^ ( M ) on the manifold M given in [gksv].

A Kratzel's integral transformation of distributions.

J. A. Barrios, J. J. Betancor (1991)

Collectanea Mathematica

In this paper we study an integral transformation introduced by E. Kratzel in spaces of distributions. This transformation is a generalization of the Laplace transform. We employ the usually called kernel method. Analyticity, boundedness, and inversion theoremes are established for the generalized transformation.

A limit involving functions in W 0 1 , p ( Ω )

Biagio Ricceri (1999)

Colloquium Mathematicae

We point out the following fact: if Ω ⊂ ℝ n is a bounded open set, δ>0, and p>1, then l i m → 0 + i n f ∈ V ∫ Ω | ∇ ( x ) | p d x = ∞ , where V = ∈ W 0 1 , p ( Ω ) : m e a s ( x ∈ Ω : | ( x ) | > δ ) > .

A multidimensional distribution sampling theorem

Francisco Javier González Vieli (2011)

Commentationes Mathematicae Universitatis Carolinae

Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions.

A new of looking at distributional estimates; applications for the bilinear Hilbert transform.

Dimitriy Bilyk, Loukas Grafakos (2006)

Collectanea Mathematica

Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...

A Note on Multipliers for Integrable Boehmians

Nemzer, Dennis (2009)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05The product of an entire function satisfying a growth condition at infinity and an integrable Boehmian is defined. Properties of this product are investigated.

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