353 research outputs found
Stieltjes transforms defined by C0-semigroups
AbstractIn this paper we use the resolvent semigroup associated to a C0-semigroup to introduce the vector-valued Stieltjes transform defined by a C0-semigroup. We give new results which extend known ones in the case of a scalar generalized Stieltjes transform. We work with the vector-valued Weyl fractional calculus to present a deep connection between both concepts
Fine scales of decay of operator semigroups
Motivated by potential applications to partial differential equations, we
develop a theory of fine scales of decay rates for operator semigroups. The
theory contains, unifies, and extends several notable results in the literature
on decay of operator semigroups and yields a number of new ones. Its core is a
new operator-theoretical method of deriving rates of decay combining
ingredients from functional calculus, and complex, real and harmonic analysis.
It also leads to several results of independent interest.Comment: Version 2 includes numerous minor corrections, and is the authors'
final version. The pape will be published in the Journal of the European
Mathematical Society in April 201
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
Product formulas in functional calculi for sectorial operators
We study the product formula in the framework of
(unbounded) functional calculus of sectorial operators . We give an abstract
result, and, as corollaries, we obtain new product formulas for the holomorphic
functional calculus, an extended Stieltjes functional calculus and an extended
Hille-Phillips functional calculus. Our results generalise previous work of
Hirsch, Martinez and Sanz, and Schilling.Comment: This is the authors accepted manuscript for a paper being published
in Mathematische Zeitschrift. The final publication is available at Springer
via http://dx.doi.org/10.1007/s00209-014-1378-
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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