215 research outputs found
Tensor product in symmetric function spaces
A concept of multiplicator of symmetric function space concerning to
projective tensor product is introduced and studied. This allows to obtain some
concrete results. In particular, the well-known theorem of R. O'Neil about the
boundedness of tensor product in the Lorentz spaces L_{p,q} is discussed.Comment: 17 page
On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p
Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes
of) p-integrable functions on [0,1]. It is known that a sequence of independent
copies of a mean zero random variable f from L_p spans in L_p a subspace
isomorphic to some Orlicz sequence space l_M. We present precise connections
between M and f and establish conditions under which the distribution of a
random variable f whose independent copies span l_M in L_p is essentially
unique.Comment: 14 pages, submitte
Best constants in Rosenthal-type inequalities and the Kruglov operator
Let be a symmetric Banach function space on with the Kruglov
property, and let , be an arbitrary
sequence of independent random variables in . This paper presents sharp
estimates in the deterministic characterization of the quantities
in terms of the sum of disjoint copies of individual terms of
. Our method is novel and based on the important recent advances in
the study of the Kruglov property through an operator approach made earlier by
the authors. In particular, we discover that the sharp constants in the
characterization above are equivalent to the norm of the Kruglov operator in
.Comment: Published in at http://dx.doi.org/10.1214/10-AOP529 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On unconditionality of fractional Rademacher chaos in symmetric spaces
We study density estimates of an index set , under which
unconditionality (or even a weaker property of the random unconditional
divergence) of the corresponding Rademacher fractional chaos in
a symmetric space implies its equivalence in to the canonical basis in
. In the special case of Orlicz spaces , unconditionality of this
system is also equivalent to the fact that a certain exponential Orlicz space
embeds into .Comment: to appear in Izv. RA
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