On a theorem of Gelfand and its local generalizations

Driss Drissi

Displaying similar documents to “On a theorem of Gelfand and its local generalizations”

$B M O_{ψ}$ -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 $B M O_{ψ}$ - $L_{\infty}$ -estimates, and arrives at $L_{p}$ - $L_{p}$ -estimates, or more generally, at estimates between K-functionals from interpolation theory.

A new Taylor type formula and $C^{\infty}$ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

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The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have $C^{\infty}$ extensions from any subpolysector; the Gevrey case is included.

Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

J. García-Cuerva, K. Kazarian (1994)

Studia Mathematica

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We study sufficient conditions on the weight w, in terms of membership in the $A_{p}$ classes, for the spline wavelet systems to be unconditional bases of the weighted space $H^{p} (w)$ . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.

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...

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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:...

Extension of multilinear mappings on Banach spaces

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

Studia Mathematica

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Measures and lacunary sets

Pascal Lefèvre (1999)

Studia Mathematica

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We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.

A characterization of some weighted norm inequalities for the fractional maximal function

Richard Wheeden (1993)

Studia Mathematica

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A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L_{v}^{p} (X)$ to $L_{w}^{q} (X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.

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 $L^{1}$ ...

Quasi-multipliers of the algebra of approximable operators and its duals

Michael Grosser (1997)

Studia Mathematica

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Let A be the Banach algebra $K_{0} (X)$ of approximable operators on an arbitrary Banach space X. For the spaces of all bilinear continuous quasi-multipliers of A resp. its dual A* resp. its bidual A**, concrete representations as spaces of operators are given.

On the size of approximately convex sets in normed spaces

S. Dilworth, Ralph Howard, James Roberts (2000)

Studia Mathematica

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Let X be a normed space. A set A ⊆ X is approximately convexif d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with $ℋ (A, C o (A)) \geq l o g_{2} n - 1$ and $d i a m (A) \leq C \sqrt n {(l n n)}^{2}$ , where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group

Silvia Secco (1999)

Studia Mathematica

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$L^{p}$ - $L^{q}$ boundedness properties are obtained for operators defined by convolution with measures supported on certain curves on the Heisenberg group. We find the curvature condition for which the type set of these operators can be the full optimal trapezoid with vertices A=(0,0), B=(1,1), C=(2/3,1/2), D=(1/2,1/3). We also give notions of right curvature and left curvature which are not mutually equivalent.