127 research outputs found
Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls
We characterize the Carleson measures for the Drury-Arveson Hardy space and
other Hilbert spaces of analytic functions of several complex variables. This
provides sharp estimates for Drury's generalization of Von Neumann's
inequality. The characterization is in terms of a geometric condition, the
"split tree condition", which reflects the nonisotropic geometry underlying the
Drury-Arveson Hardy space
The characterization of the Carleson measures for analytic Besov spaces: a simple proof
We give a simple proof of the characterization of the Carleson measures for
the weighted analytic Besov spaces. Such characterization provides some
information on the radial variation of an analytic Besov function.Comment: 12 page
Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces
We investigate connections between potential theories on a Ahlfors-regular
metric space X, on a graph G associated with X, and on the tree T obtained by
removing the "horizontal edges" in G. Applications to the calculation of set
capacity are given.Comment: 45 pages; presentation improved based on referee comment
An Interesting Class of Operators with unusual Schatten-von Neumann behavior
We consider the class of integral operators Q_\f on of the form
(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and
sufficient conditions on to insure that is bounded, compact,
or in the Schatten-von Neumann class \bS_p, . We also give
necessary and sufficient conditions for to be a finite rank
operator. However, there is a kind of cut-off at , and for membership in
\bS_{p}, , the situation is more complicated. Although we give
various necessary conditions and sufficient conditions relating to
Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient
conditions. In the most important case , we have a necessary condition and
a sufficient condition, using and modulus of continuity,
respectively, with a rather small gap in between. A second cut-off occurs at
: if \f is sufficiently smooth and decays reasonably fast, then \qf
belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to
\bS_{1/2} unless \f=0.
We also obtain results for related families of operators acting on
and .
We further study operations acting on bounded linear operators on
related to the class of operators Q_\f. In particular we
study Schur multipliers given by functions of the form and
we study properties of the averaging projection (Hilbert-Schmidt projection)
onto the operators of the form Q_\f.Comment: 87 page
Composition Operators and Endomorphisms
If is an inner function, then composition with induces an
endomorphism, , of that leaves
invariant. We investigate the structure of the
endomorphisms of and that implement
through the representations of and
in terms of multiplication operators on
and . Our analysis, which is based on work
of R. Rochberg and J. McDonald, will wind its way through the theory of
composition operators on spaces of analytic functions to recent work on Cuntz
families of isometries and Hilbert -modules
More than just a bracelet: the use of material symbolism to communicate love
There is growing recognition of the place of love in residential care for children (Smith, 2009). This paper is a critical analysis of a range of existing research on residential child care as well as studies of material culture and of care relationships more broadly. It argues that, despite increasing regulation and surveillance, adults and children find ways to show and feel love in the context of residential care. Whilst love may be regarded as something to be avoided or indeed prohibited in an adult/child care setting these deep bonds find expression in the everyday life of the children's home. By looking at love in this embodied way, the 'realness' of material things to assert connection and recognition of love (Layne, 2000) is examined. As Gorenstein (1996, p.8) suggests 'objects...[are] the perfect vehicles for conveying themes that are not commonly accepted in a community'. The paper emphasises the recognition of these symbolic and metaphorical forms of communication in practice
Invariance of capacity under quasisymmetric maps of the circle: an easy proof
A combinatorial proof of the invariance of capacity under quasisymmetric maps of the unit circle is given
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