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We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential...

Discrete analogues of singular and maximal Radon transforms.

Wainger, Stephen (1998)

Documenta Mathematica

Discrete fractional calculus with the nabla operator.

Atici, F.M., Eloe, P. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Discrete limit theorems for the Laplace transform of the Riemann zeta-function

Roma Kačinskaitė, Antanas Laurinčikas (2005)

Acta Mathematica Universitatis Ostraviensis

In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.

Discrete limit theorems for the Mellin transform of the Riemann zeta-function

Violeta Balinskaitė, Antanas Laurinčikas (2008)

Acta Arithmetica

Distributional fractional powers of the Laplacean. Riesz potentials

Celso Martínez, Miguel Sanzi, Francisco Periago (1999)

Studia Mathematica

For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, $({(- Δ)}^{α} u, ϕ) = (u, {(- Δ)}^{α} ϕ)$ , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada, Jasson Vindas (2013)

Czechoslovak Mathematical Journal

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...

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Displaying 1 – 18 of 18

Das Wachstumsverhalten ganzer Funktionen unter Voraussetzungen über ihre Laplace-Transformierte.

Degrés de liberté des moyennes de convolution préservant la réalité

Démonstration probabiliste d'une identité de convolution

Der Konjugiertenoperator auf rearrangement-invarianten Funktionenräumen.

Derangements and asymptotics of the Laplace transforms of large powers of a polynomial.

Derivatives of noninteger order and their applications [Book]

Die Laguerre-Pinney-Transformation.

Different aspects of differentiability [Book]

Directional operators and mixed norms.