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Besov spaces and 2-summing operators

M. A. Fugarolas (2004)

Colloquium Mathematicae

Let Π₂ be the operator ideal of all absolutely 2-summing operators and let I m be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of I m . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also consider the...

Boundary regularity of admissible operators.

Christoph H. Lampert (2005)

Publicacions Matemàtiques

In strictly pseudoconvex domains with smooth boundary, we prove a commutator relationship between admissible integral operators, as introduced by Lieb and Range, and smooth vector fields which are tangential at boundary points. This makes it possible to gain estimates for admissible operators in function spaces which involve tangential derivatives. Examples are given under with circumstances these can be transformed into genuine Sobolev- and Ck-estimates.

Bounded projections in weighted function spaces in a generalized unit disc

A. H. Karapetyan (1995)

Annales Polonici Mathematici

Let M m , n be the space of all complex m × n matrices. The generalized unit disc in M m , n is >br>    R m , n = Z M m , n : I ( m ) - Z Z * i s p o s i t i v e d e f i n i t e . Here I ( m ) M m , m is the unit matrix. If 1 ≤ p < ∞ and α > -1, then L α p ( R m , n ) is defined to be the space L p R m , n ; [ d e t ( I ( m ) - Z Z * ) ] α d μ m , n ( Z ) , where μ m , n is the Lebesgue measure in M m , n , and H α p ( R m , n ) L α p ( R m , n ) is the subspace of holomorphic functions. In [8,9] M. M. Djrbashian and A. H. Karapetyan proved that, if R e β > ( α + 1 ) / p - 1 (for 1 < p < ∞) and Re β ≥ α (for p = 1), then     f ( ) = T m , n β ( f ) ( ) , R m , n , where T m , n β is the integral operator defined by (0.13)-(0.14). In the present paper, given 1 ≤ p <...

Boundedness properties of fractional integral operators associated to non-doubling measures

José García-Cuerva, A. Eduardo Gatto (2004)

Studia Mathematica

The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling...

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