1,198 research outputs found
ON SOME PROPERTIES OF THE CLASS OF STATIONARY SETS
International audienceSome new properties of the stationary sets (defined by G. Pisier in [12]) are studied. Some arithmetical conditions are given, leading to the non- stationarity of the prime numbers. It is shown that any stationary set is a set of continuity. Some examples of "large" stationary sets are given, which are not sets of uniform convergence
Compact composition operators on Bergman-Orlicz spaces
We construct an analytic self-map of the unit disk and an Orlicz
function for which the composition operator of symbol is compact
on the Hardy-Orlicz space , but not compact on the Bergman-Orlicz space
. For that, we first prove a Carleson embedding theorem,
and then characterize the compactness of composition operators on
Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that
this Carleson function is equivalent to the Nevanlinna counting function of
order 2.Comment: 32 page
Compact composition operators on the Dirichlet space and capacity of sets of contact points
In this paper, we prove that for every compact set of the unit disk of
logarithmic capacity 0, there exists a Schur function both in the disk algebra
and in the Dirichlet space such that the associated composition operator is in
all Schatten classes (of the Dirichlet space), and for which the set of points
whose image touches the unit circle is equal to this compact set. We show that
for every bounded composition operator on the Dirichlet space and for every
point of the unit circle, the logarithmic capacity of the set of point having
this point as image is 0. We show that every compact composition operator on
the Dirichlet space is compact on the gaussian Hardy-Orlicz space; in
particular, it is in every Schatten class on the usual Hilbertian Hardy space.
On the other hand, there exists a Schur function such that the associated
composition operator is compact on the gaussian Hardy-Orlicz space, but which
is not even bounded on the Dirichlet space. We prove that the Schatten classes
on the Dirichlet space can be separated by composition operators. Also, there
exists a Schur function such that the associated composition operator is
compact on the Dirichlet space, but in no Schatten class
Thin sets of integers in Harmonic analysis and p-stable random Fourier series
We investigate the behavior of some thin sets of integers defined through
random trigonometric polynomial when one replaces Gaussian or Rademacher
variables by p-stable ones, with 1 < p < 2. We show that in one case this
behavior is essentially the same as in the Gaussian case, whereas in another
case, this behavior is entirely different
The canonical injection of the Hardy-Orlicz space into the Bergman-Orlicz space
We study the canonical injection from the Hardy-Orlicz space into
the Bergman-Orlicz space .Comment: 21 page
Some new properties of composition operators associated with lens maps
We give examples of results on composition operators connected with lens
maps. The first two concern the approximation numbers of those operators acting
on the usual Hardy space . The last ones are connected with Hardy-Orlicz
and Bergman-Orlicz spaces and , and provide a negative answer
to the question of knowing if all composition operators which are weakly
compact on a non-reflexive space are norm-compact.Comment: 21 page
Weak compactness and Orlicz spaces
We give new proofs that some Banach spaces have Pe{\l}czy\'nski's property
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