Hausdorff matrices as bounded operators over $l$

Hausdorff Matrices as Bounded Operators over /

A necessary and sufficient condition is obtained for an arbitrary Hausdorff matrix to belong to B(l). It is then shown that every conservative quasi-Hausdorff matrix is of type M. Let (H, u) denote the Hausdorff method with generating sequence ¡x = {/L,}, / = {{xn} \2„\xn\ < oo}, B(l) the algebra of bounded linear operators on /. A necessary and sufficient condition is obtained for an arbitrary...

Generalized Hausdorff Matrices as Bounded Operators on ! p*

N6r lund matrices as bounded operators on lp

Group invariance and L-bounded operators

In this paper we consider translation invariant operators with additional symmetry coming from group actions. As the classic Hilbert and Riesz transforms can be characterized up to scalar by means of relative invariance of conformal transformation groups, certain multiplier operators are characterized by relative invariance of some other affine subgroups. In this article, we formalize a geometr...

Boundedness of Multidimensional Hausdorff Operators on L and H Spaces

For a wide family of multivariate Hausdorff operators, a new stronger condition for the boundedness of an operator from this family on the real Hardy space H by means of atomic decomposition. 2000 Mathematics Subject Classification. Primary 47B38, 42B10; Secondary 46E30.