Displaying similar documents to “Triebel-Lizorkin spaces on spaces of homogeneous type”

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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...

On sharp reiteration theorems and weighted norm inequalities

Jesús Bastero, Mario Milman, Francisco Ruiz (2000)

Studia Mathematica

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We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.

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.

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.