$BMO_ψ$-spaces and applications to extrapolation theory

Stefan Geiss

Displaying similar documents to “ $B M O_{ψ}$ -spaces and applications to extrapolation theory”

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 ${P (| X |}_{k} \geq t) = e x p (- N_{k} (t))$ , 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.

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 $L^{1}$ ...

Discrete Hardy spaces

Santiago Boza, María Carro (1998)

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We study various characterizations of the Hardy spaces $H^{p} (ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^{p} (ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.

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.

On certain nonstandard Calderón-Zygmund operators

Steve Hofmann (1994)

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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.

Subanalytic version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (1997)

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

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

Silvia Secco (1999)

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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 condition implying boundedness and VMO for a function f

Michelangelo Franciosi (1997)

Studia Mathematica

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Some boundedness and VMO results are proved for a function f integrable on a cube $Q_{0}$ , starting from an integral bound.

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:...

Singularities of triples of vector fields on $R^{4}$ : the focusing stratum

Piotr Mormul (1988)

Studia Mathematica

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The boundary Harnack principle for the fractional Laplacian

Krzysztof Bogdan (1997)

Studia Mathematica

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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.

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.

Displaying similar documents to “ B M O ψ -spaces and applications to extrapolation theory”

Displaying similar documents to “ $B M O_{ψ}$ -spaces and applications to extrapolation theory”