Displaying similar documents to “Quasi-multipliers of the algebra of approximable operators and its duals”

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E. Albrecht, W. Ricker (1998)

Studia Mathematica

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The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in L p ( ℝ N ) . The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi:...

Complemented ideals of group algebras

Andrew Kepert (1994)

Studia Mathematica

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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...

B M O ψ -spaces and applications to extrapolation theory

Stefan Geiss (1997)

Studia Mathematica

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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 ∞ -estimates, and arrives at L p - L p -estimates, or more generally, at estimates between K-functionals from interpolation theory.

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

Guozhen Lu, Richard Wheeden (2000)

Studia Mathematica

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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 ...

On certain nonstandard Calderón-Zygmund operators

Steve Hofmann (1994)

Studia Mathematica

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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.

Besov spaces on symmetric manifolds—the atomic decomposition

Leszek Skrzypczak (1997)

Studia Mathematica

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We give the atomic decomposition of the inhomogeneous Besov spaces defined on symmetric Riemannian spaces of noncompact type. As an application we get a theorem of Bernstein type for the Helgason-Fourier transform.

Moment inequalities for sums of certain independent symmetric random variables

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

Studia Mathematica

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This paper gives upper and lower bounds for moments of sums of independent random variables ( X k ) which satisfy the condition P ( | X | k ≥ 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.

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

Krzysztof Bogdan, Tomasz Byczkowski (1999)

Studia Mathematica

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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.