Displaying similar documents to “Volume approximation of convex bodies by polytopes - a constructive method”

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.

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 ( A , C o ( A ) ) l o g 2 n - 1 and d i a m ( A ) C 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.

A new Taylor type formula and C 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 extensions from any subpolysector; the Gevrey case is included.

Representations of the spaces C ( N ) H k , p ( N )

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

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We give a representation of the spaces C ( N ) H k , p ( N ) as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that C ( N ) H k , 2 ( N ) is isomorphic to the sequence space s l 2 ( l 2 ) , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

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 ...

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.

Integral operators and weighted amalgams

C. Carton-Lebrun, H. Heinig, S. Hofmann (1994)

Studia Mathematica

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For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from q ̅ ( L v p ̅ ) into q ( L u p ) . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted L p -spaces. Amalgams of the form q ( L w p ) , 1 < p,q < ∞ , q ≠ p, w A p , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.

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.

Uniqueness of complete norms for quotients of Banach function algebras

W. Bade, H. Dales (1993)

Studia Mathematica

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We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra L 1 ( G ) of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients A ( Γ ) / J ( E ) ¯ arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed....

Subanalytic version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (1997)

Studia Mathematica

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For any subanalytic C k -Whitney field (k finite), we construct its subanalytic C k -extension to n . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.

Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Christopher Boyd (1993)

Studia Mathematica

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For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that G ( U ) i ' = ( ( U ) , τ δ ) . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the τ 0 and τ ω topologies on ℋ (U).