94 research outputs found
Littlewood-Paley-Stein type square functions based on Laguerre semigroups
We investigate g-functions based on semigroups related to multi-dimensional
Laguerre function expansions of convolution type. We prove that these operators
can be viewed as Calderon-Zygmund operators in the sense of the underlying
space of homogeneous type, hence their mapping properties follow from the
general theory.Comment: 30 page
On ergodicity of some Markov processes
We formulate a criterion for the existence and uniqueness of an invariant
measure for a Markov process taking values in a Polish phase space. In
addition, weak- ergodicity, that is, the weak convergence of the ergodic
averages of the laws of the process starting from any initial distribution, is
established. The principal assumptions are the existence of a lower bound for
the ergodic averages of the transition probability function and its local
uniform continuity. The latter is called the e-property. The general result is
applied to solutions of some stochastic evolution equations in Hilbert spaces.
As an example, we consider an evolution equation whose solution describes the
Lagrangian observations of the velocity field in the passive tracer model. The
weak- mean ergodicity of the corresponding invariant measure is used to
derive the law of large numbers for the trajectory of a tracer.Comment: Published in at http://dx.doi.org/10.1214/09-AOP513 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Calder\'on-Zygmund operators in the Bessel setting for all possible type indices
In this paper we adapt the technique developed in [17] to show that many
harmonic analysis operators in the Bessel setting, including maximal operators,
Littlewood-Paley-Stein type square functions, multipliers of Laplace or
Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as,
Calder\'on-Zygmund operators for all possible values of type parameter
in this context. This extends the results obtained recently in [7],
which are valid only for a restricted range of .Comment: 12 page
Multipliers of Laplace transform type in certain Dunkl and Laguerre settings
We investigate Laplace type and Laplace-Stieltjes type multipliers in the
-dimensional setting of the Dunkl harmonic oscillator with the associated
group of reflections isomorphic to and in the related context
of Laguerre function expansions of convolution type. We use Calder\'on-Zygmund
theory to prove that these multiplier operators are bounded on weighted ,
, and from to weak .Comment: 12 page
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
We consider several harmonic analysis operators in the multi-dimensional
context of the Dunkl Laplacian with the underlying group of reflections
isomorphic to (also negative values of the multiplicity
function are admitted). Our investigations include maximal operators,
-functions, Lusin area integrals, Riesz transforms and multipliers of
Laplace and Laplace-Stieltjes transform type. Using the general
Calder\'on-Zygmund theory we prove that these objects are bounded in weighted
spaces, , and from into weak .Comment: 26 pages. arXiv admin note: text overlap with arXiv:1011.3615 by
other author
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