Averaging theorems for linear operators in compact groups and semigroups

G. Murphy; T. West

Displaying similar documents to “Averaging theorems for linear operators in compact groups and semigroups”

Moment inequalities for sums of certain independent symmetric random variables

P. Hitczenko, S. Montgomery-Smith, K. Oleszkiewicz (1997)

Studia Mathematica

Similarity:

This paper gives upper and lower bounds for moments of sums of independent random variables $(X_{k})$ which satisfy the condition ${P (| X |}_{k} \geq t) = e x p (- N_{k} (t))$ , where $N_{k}$ are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which $N (t) = {| t |}^{r}$ for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N.

Complemented ideals of group algebras

Andrew Kepert (1994)

Studia Mathematica

Similarity:

The existence of a projection onto an ideal I of a commutative group algebra $L^{1} (G)$ depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously...

High order representation formulas and embedding theorems on stratified groups and generalizations

Guozhen Lu, Richard Wheeden (2000)

Studia Mathematica

Similarity:

We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable $L^{1}$ to $L^{1}$ Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and $L^{1}$ ...

$B M O_{ψ}$ -spaces and applications to extrapolation theory

Stefan Geiss (1997)

Studia Mathematica

Similarity:

We investigate a scale of $B M O_{ψ}$ -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with $B M O_{ψ}$ - $L_{\infty}$ -estimates, and arrives at $L_{p}$ - $L_{p}$ -estimates, or more generally, at estimates between K-functionals from interpolation theory.

On certain nonstandard Calderón-Zygmund operators

Steve Hofmann (1994)

Studia Mathematica

Similarity:

We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in $ℝ^{n}$ related to the first Calderón commutator, but with a kernel which is far less regular.

Extension of multilinear mappings on Banach spaces

Pablo Galindo, Domingo Garciá, Manuel Maestre, Jorge Mujica (1994)

Studia Mathematica

Similarity:

The boundary Harnack principle for the fractional Laplacian

Krzysztof Bogdan (1997)

Studia Mathematica

Similarity:

We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.

Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains

Krzysztof Bogdan, Tomasz Byczkowski (1999)

Studia Mathematica

Similarity:

The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.

On an additive property of squares and primes

Imre Ruzsa (1988)

Acta Arithmetica

Similarity:

Some integral and maximal operators related to starlike sets

Sagun Chanillo, David Watson, Richard Wheeden (1993)

Studia Mathematica

Similarity:

We prove two-weight norm estimates for fractional integrals and fractional maximal functions associated with starlike sets in Euclidean space. This is seen to include general positive homogeneous fractional integrals and fractional integrals on product spaces. We consider both weak type and strong type results, and we show that the conditions imposed on the weight functions are fairly sharp.